1. Visit the wiki first... we can type it here again, with our personal opinions possibly conflicting each other, maybe with mistakes and things omitted; or you can read those in wiki, which have been debated and revised.

http://wiki.spiralknights.com/Starting_out
Bomb: http://wiki.spiralknights.com/Bombing_Guide
Sword: http://wiki.spiralknights.com/Swordmaster_Guide
Gun: http://wiki.spiralknights.com/Gunslinger_Guide
Shield: http://wiki.spiralknights.com/Shieldbearer_Guide

In short you should read about Alchemy paths on wiki; except Radiant Sun Shard, everything that cannot be upgraded to 5* should be ignored. And while Cutter is not a really bad line of weapons, it takes a bit of care to use in T2 and beyond, and there are always better choices.

2. How about all of them? FSC > JK > RT. JK and RT should be very similar in crown output now, but there are still significantly more enemies in JK, so if you want heat too, go there. Do Basil runs when you are bored of the bosses, and there are gates with lots of arenas/graveyards.

3. Start looking at AH. Sort by starting bid and buy out price, see how many listings and bids are there. Come to your own conclusions about what are popular/profitable. The market is always changing - everyone knows a certain stuff is profitable, then suddenly you'd have a lot more on sale and undercutting each other, and profits go down. So observe the market and make your own decisions.

4. Read the guides mentioned in 1. This main point is this game is about not getting hit.

Well, Arenas are nerfed a bit, but T2 arenas Still give alot (1000 cr~~)

For T2, Roarmulus And Jelly King are the farming area. Roarmulus Twins, I have found out on average it gives EXACTLY the same Heat, Cr, blah blah blehhh On average, its 2300 cr per first 2 levels, and 2500 if you do the boss.

Vanaduke is the farming area for T3, and a few tips when you get to 4*, its hard to get a party in the clockworks now, and fire kills a lot.

Chilled to the bone and work for idle hands... well, they are hard even with my 4* armor, but one day... you will get a good party :)

The emberbreak set... sadly, it ends at 3*. Get wolver after that. The cutter itself isnt a bad weap, but it is bad in Lockdown. Oh, and go for the Vile Striker side, not the hunting blade. its only better for beasts, and beasts suck already :D

When I said 'don't pick the cutter', what I meant was that it is hard to use correctly, not that it's crap. :P
Most people I have seen who use it just rush in and get themselves killed whilst attempting to complete a combo.
It has a lower survivability if used incorrectly and normal damage, which is why it isn't always the best choice.
I am aware it can be devastating when used against Vanaduke's mask, for starters, but it isn't really a weapon I would recommend for someone just starting out in the game.
If you do work at it, it'll be great once you've mastered it, but the learning curve is pretty steep and there are other weapons easier to use for a new player just starting out.

(Also, just for future reference... I'm a girl...)

Warning: Long Post! There is a TL;DR at the end

I myself am a Hybrid player, but I find it's best to not try to wield a lot of weapon types at once. In my experience the best combos for me are (in order of ones that work best for me):
- 2 Swords, 2 Guns
- 2 Swords, 1 Gun, 1 Bomb
- 1 Sword, 3 Guns
- 1 Sword, 1 Gun, 2 Bombs
- 2 Swords, 2 Bombs

Guns and Swords naturally go together because of how easily you can swap from gun to sword or sword to gun. Bombs are hard to work in because they require charging. It's hard to constantly switch to a bomb and drop one quickly, before returning to a sword or gun.

As for equipment suggestions:

Swords:
I'm a Brandish guy myself. I use an Acheron and Glacius (Nightblade and Iceburst Brandish at 3*) for my Shadow Damage and Elemental Damage. The Sealed Swords tend to be more expensive, but the Divine Avenger and Gran Faust are also respectable replacements. I prefer the more offensive nature of Brandishes over the defensive Sealed Swords. However, a good Heavy Sword is nice if you're focusing heavily on guns and bombs, because they can easily knock back a large group of enemies to give you some breathing room. My piercing weapon of choice is the Final Flourish, but the Barbarous Thorn Blade (Snarble Barb at 2*) is almost the same. I don't suggested the Snarble Barb line due to the recipes being expensive.

Guns:
I have the most fun when I'm quickly swapping between fast Brandishes and rapid-fire Antiguas. The Antigua Lines work really well with swords, because you can easily swap to one, spray out a few shots, and then go back to slashing without having to really worry about accuracy or reloading. I've gotten used to using Antigua shots to slightly damage Zombies while using their breath attack, which abruptly makes them stop using said attack. If you want a gun as your primary weapon, Alchemers are your best bet. Umbra Driver and any elemental Alchemer will do (I use Prismatech, but I'm working on Voltech). They feel really weak until about 4*, but they do pull out some serious damage late game. My record is killing 3 Zombies who were at full health with 1 Nova Driver Charge Shot (3 man party too). It takes some time to get used to the weird hitbox and bizarre but predictable nature of ricochets, but once you do the Alchemers can really do a lot of damage. As for piercing guns, the Callahan is my main. However, the Blitz is far more useful in the tier 3 boss area, Firestorm Citadel, because the charge shot has one of the highest (if not THE highest) DPS.

The final gun that deserves a special note is the Pulsar. It's worth getting a Pulsar from Roarmulus Tokens, and then upgrading it to Kilowatt Pulsar, and eventually Polaris. The Pulsar is a dangerous weapon, not just for your enemies. It has unpredictable knockback and is annoyingly blinding. It's easily spammed, but when you do easily spam it, it really becomes a hassle for allies and anyone who focuses on close-range combat (like swords and maybe bombs). I have two sayings with Pulsars that I tend to tell aspiring gunners: 1) Spam with taste (Don't pull out your Pulsar at the start of a battle, and then never put it away throughout the rest of the floor) 2) When the s***t hits the fan: Polaris (use Pulsars as a last resort in emergencies, not as a primary weapon).

Bombs
Most bombers take a support role with statuses. The most common status bomb that I see is the Shivermist Buster (Freezing Vaporizer). People will be prepared to BEG for a shiver in Firestorm Citadel (last boss area), while at the same time, using shiver isn't incredibly difficult (just have to remain focused). Despite this, Shiver is a bit situational, and isn't used that much outside of Firestorm Citadel. I use Voltaic Tempest (Static Capacitor) a lot for its damage, its immobilization of enemies and it's one of the most dangerous weapons in Lockdown (PvP). The recipes are a bit expensive though. Venom Veiler (Toxic Vaporizer) is rare, but I find rather useful as well when you're up against healers. Now that I think about it, all the status bombs are really nice, and worth looking into. I highly recommend at least the Shiver for use late game, and Voltaic Tempest is the one I use the most outside of Firestorm Citadel.

For damage bombers, the most common bombs are Radiant Sun Shards (Crystal Bomb) and Dark Briar Barrage (Spine Cone). DBB is your main piercing bomb, while RSS is just awesome vs Undead and Fiends, despite being 4*. If you have Operation Crimson Hammer, the shadow bomb that you get as a reward is one of the few shadow bombs that does good DPS.

As a final note, the rarest but most loved bombs (at least for swordsmen/me) are the Vortex Bombs. They give a big movement penalty while charging, but they work incredibly well with swordsmen and alchemers even. I always love a good Vortex Bomb in almost every situation I encounter for the awesome crowd control abilities.

For armor sets, I'm going to be quick with this:

Yes, you want at least one set for every damage type you go up against. I suggest these:
Sword: Wolver -> Skolver Set (Pierce)
Gun: Gunslinger -> Shadowsun Set (Pierce/Shadow)
Bomb: Bomber -> Volcanic Demo Set (Elemental)

Those are three really good armor sets for bombs, guns, and swords. If you can, work on the other 5* versions of the same armor lines. I tend to mix and match them myself, or just have my armor buff one of my weapon types and use Trinkets/UVs to buff the other(s).

As for shields, I use 4 shields overall, and you really only need one shield for each damage type:

Barbarous Thorn Shield (Bristling Buckler)
Grey Owlite Shield (Owlite Shield)
Crest of Almire (Burnt Crest) (This is a reward from the Firestorm Citadel boss, so I suggest a Skelly Shield instead)
Swiftstrike Bucker (3*)

The Swiftstrike Buckler is a special shield that is only best used in places you know really well. It can't take a punch, but it gives everything you have Attack Speed Increase High (despite the description saying Swords only, it does work on Guns).

Moving onto your next question: profit!

I've been running tier 2 arcade runs lately, despite being a tier 3 knight. The key is to get good at reading a Gate Map. Look up Gate Map on the wiki for a basic overview. You want to skim through the tier 2 areas, and go to the gate with both a boss and as many arenas between Moorcraft and Emberlight. Try to hit as many arenas as you can, as well as the boss. It's about 80 mist per run, but I'm getting about 8,000 crowns per run (with 3 arenas). I also suggest the arcade because of Basil. At d13, you will find a Stranger named Basil who sells recipes. A lot of recipes can be obtained at the Hall of Heroes, but there are a select few that don't and sell for a MASSIVE profit on the Auction House. The most reliably selling ones are the Twisted Spine Cone (about 9,000 on the AH), the Twisted Snarble Barb (close to 12,000 on the AH), the Twisted Targe (around 14,000 on the AH), and the Kilowatt Pulsar (slightly above 14,000 on the AH). All of these recipes are 4,000 from Basil (if you get lucky), so it's a really easy way to get profit. It relies on a bit of luck, but it has high rewards for a rather small risk (Especially because you can use that 8k per run to get 100 CE and do the run again with 20 CE net profit. It's a bit tedious, but it's sustainable and the profit from recipes can make it worthwhile).

Now material trading!

Look up the recipes for Wolver Armor, Brandishes, Flourishes, and Alchemers. Those materials are constantly in demand due to high level players constantly ragecrafting said items for a chance at a good UV. Most of the materials are hovering at around 100 per (Shards are like 10-20 per), so you can easily make a bit off to the side with them. Be sure to check the price of an item on the Auction House, BEFORE you post your own offer. Then, post your own offer at one crown less or even at the same price as the lowest offer on the AH.

If you want to advertise (which I don't recommend), use either /1 MESSAGE to tell everyone in Haven or use Trade Chat. Trade Chat can be joined by typing /join 2 and then you can type /2 MESSAGE to tell everyone on Trade Chat. As you can tell by the name, it's for people who want to buy or sell items. Also, for future reference, you will see a lot of WTB and WTS. WTB means Willing To Buy, WTS means Willing To Sell, and ocasionally you'll see WTT which is Willing To Trade.

Also, I suggest you use your tokens for crowns too. Tokens that end with Spark can be traded to Brinks for some rare mats. I spent a while long ago writing down mat names and their prices on the Auction House. The market does change, so it is rendered a bit obsolete now. Recently, I've found Philoso Feathers, which are 20 Grim Sparks, go for a little more than 2,000 crowns each on the Auction House. Drake Scales also sell well if I'm not mistaken for Primal Sparks.

As for the missions you're having trouble with:

I highly suggest some Elemental and Piercing Weapons. A Flourish is about 1000 crowns for the 2* weapon on the Auction House, and it is an incredibly useful weapon. Piercing will crit against Fiends (as shown with brown-ish red/yellow numbers). Elemental Weapons will crit against Undead, so I suggest you upgrade a Brandish to one of the elemental lines (Iceburst, Shockburst, or Fireburst). All three of them just do a different status on their charge, with none being better than the other. It's personal preference and you'll get used to whatever one you pick.

TL;DR:

Equipment:
- Brandish -> Acheron and Elemental Brandish = Offense
- Sealed Sword -> Divine Avenger and Gran Faust = Defence
- Flourish -> Final Flourish
- Antigua
- Alchemer
- Pulsar
- Status Bomb
- Crystal Bomb -> Radiant Sun Shards
- Spine Cone -> Dark Briar Barrage
- Skolver Set
- Shadowsun Sun
- Volcanic Demo Set
- Bristling Buckler -> Barbarous Thorn Shield
- Owlite Shield -> Grey Owlite Shield
- Skelly Shield -> Dread Skelly Shield

Money:
- Tier 2 Recipe Runs: Buy these and sell on the AH
- - Twisted Spine Cone
- - Twisted Snarble Barb
- - Twisted Targe
- - Kilowatt Pulsar

Trade:
- Use Auction House to get price and Trade Chat to advertise

Missions:
- Get Elemental Brandish and Flourish

Mist is shared per account, unless you buy something to separate it. If someone else is using your account, even if it isn't your knight, you'll be loosing energy.

The other thing is that MIST energy regenerates at 100 energy over 22 hours. Crystal Energy does not. Crystal Energy needs to be bought (either with $$ or from other players). Mist energy will not go past 100, while Crystal Energy can go into the millions.

The CE prices changes with patches and promos. Unless there is some active drive to raise the CE price (Trust me, active attempts to lower the CE price don't work... ever), it will eventually level out.

Most of the time patches that increase the crown drop rate in certain areas (most of the time Firestorm Citadel) with cause the CE price to increase. This is because players now have more crowns, and are able to buy more CE. However, the amount of CE in the market hasn't changed. Higher demand, same (if not less) supply, thus the prices increase. The opposite is true too. Patches that decrease the crown drop rate in certain areas lower the price of CE. People have less crowns, thus aren't buying as much CE. Those who are selling CE, still want crowns and are willing to accept selling them at a lower price in order to profit.

Promos are another big influence in the market. When a good promo comes along, like the Solstice Pack, people who either have never bought before, or have the money to make several purchases, suddenly have a reason to spend a rather small amount of money to get a remarkably large amount of CE. $25 for OVER 9000 CE? Yeah that lasts for several weeks, if not months if you're conservative. Most people aren't, and, due to practically swimming in CE, are willing to casually throw it away for crowns. Supply of CE goes up, the demand goes down because more people have more CE than they know what to do with, and thus the price goes down.