I want this thread to be useful to everyone, including players like myself. In order to do that, I'd like to open with the raw facts players have gathered, as I feel this would be much more useful than just my saying "buy this here!"

USEFUL LINKS

Lancer Knight's data regarding drops:
http://wiki.spiralknights.com/Lancer_Knightz_%28Guild%29/Missions#Rariti...

Skepticraven's thread describing how good the current gates are for radiant fire crystals:
http://forums.spiralknights.com/en/node/107719

Skepticraven's data regarding the number of boxes on various levels:
https://docs.google.com/spreadsheets/d/16VBTxodPjQFluDYXzXrZ9ifIBy4x2OKa...

The bulk of reported weapon drops across the history of the game: (note that this is to be taken with a grain of salt)
http://forums.spiralknights.com/en/node/11128

The finding of a regal slime node wall, a never before seen item-
http://forums.spiralknights.com/en/node/109270

The newest mission, Dreams and Nightmares:
http://forums.spiralknights.com/en/node/109748

Here is where everything is as a rule of thumb:

To summarize all of the links together in a way that you can remember...

Orbs are found from treasure boxes in their respective areas of the game.

Fire crystals are found alongside orbs in their respective areas.

Treasure boxes are found on most levels, but particularly in the following areas:

Crowns are found primarily from monsters, and are more dependent on level + location in stratum than in tier.

Materials are found primarily from monsters, and are dependent on depth and level type.

Item drops appear to be based on where you are and how deep you are.

For more information, again, the sources are listed above and I encourage you to read through them or keep them bookmarked as a guide.

The mid-game

This is where the game requires you to find orbs first, as all of the 0/1* items and some of the 2* items are handed to you through the mission system. My honest advice for you is to just go on runs intelligently, meaning to hunt down high priority levels and go on "good runs", as well as bosses. If you see a gate with several high paying levels on it, then that's the one you should go on.

Your main priority should be orb drops. Crowns will come naturally, and you'll find recipes in the hall of heroes and on auction house from crowns. But without farming the correct areas, you won't find orbs. These areas are as outlined above. Fire crystals will also come naturally, and are typically more common than orbs in this part of the game by any rate.

If you don't find orbs and have leftover crowns from recipes, you can turn your crowns into energy and buy the orbs you need. I would recommend doing this, because there is definitely a good chance that you'll encounter a dry spell or three when farming. It's only to be expected, and it doesn't mean the game hates you or anything. Crowns on the other hand do not have any dry spells, and can free you from having to find orbs for a bit.

If you need crowns, stratum 4 is going to be your friend. Focus on finding arenas towards the end of stratum 4, and running bosses.

I NEED SHINNING FIRE CRYSTALS- you're going to have a hard time believing this but you probably don't need any shinning fire crystals yet. In tier 2, your 4* gear will be just as strong at level 1 as it is at level 10, the one exception being the charge time reduction that it picks up along the way. When you get to tier 3, you'll find MASSIVE amounts of shinning fire crystals everywhere, and will quickly have a good 15,000 left over.

The endgame

If you can run all of tier 3 competently, then farming for the lower tiered orbs is good if that's what you want to do, but not necessary as you can produce enough crowns to just flat out buy the orbs faster while farming for the one thing that matters most to you- radiant fire crystals.

And I can already hear it- "BUT I NEED ETERNAL ORBS OF-", again, you really don't need that. Even on D27 and D28 alone, you'll be finding a higher ratio of eternal orbs to radiant fire crystals, meaning that like shinning fire crystals, you'll very quickly have over 100 eternal orbs that you can't use. The solution: Disregard shinning fire crystals AND eternal orbs in favor of the one true rarity: Radiant fire crystals.

The kosher way to get radiant fire crystals is to hunt them down in D27 and D28 arenas, and then invite your friends once down there so that everyone gets them. Yes, even at 4* and as you're just entering tier 3. If there aren't any arenas, clockwork tunnels work for their danger rooms (mind the difficulty gap) and failing that firestorm citadel is always around. And failing that, you can run T2 for those rarities which will still save you some crowns.

More on firestorm citadel- players are going to make it out to be a big deal, like it's THE mission to farm and that it's THE ONLY BIG CROWN THING- and it's not. It's just not. But it's good and the benefit to it is more that there will be a party waiting for you at all times. While you enjoy going on it and learning to become master of the slag is entertaining you, you should grind it because all in all it's still a nice payout and fang of vog is an awesome trophy to have. But don't fall into the trap of playing nothing but firestorm citadel unless you really really like it. Arena hunting will be much better and more interesting than just killing slags all day.

Eventually, you'll be able to run Dreams and Nightmares which consists of 2 cheap+easy levels that you can run through and 1 slightly harder level that you can't. As soon as you can reliably speed run this level, I would recommend doing so to attain radiant fire crystals- 22-23 per run is a fairly solid number for what comes out to about 2 levels worth of challenge, compared to running the entire arcade for slightly more, depending on the levels. An important thing to keep in mind is that Dreams and Nightmares does not give many materials or crowns. If you're interested in either of these, you may want to stick to other levels.

Your average farming day goes as follows:

1. If you need something specific like materials, boss tokens or prestige, go on a run for those.
2. If there is an arena etc. in an applicable area that interests you, go on that arcade gate.
3. If you have a mission that you like and that gives you what you need, go for it.
4. Do a random run or farm a random area of your choosing for crowns.

Remember to actually have while playing fun video games

Time flies when you're having fun.

This is by far the most important part of farming. If you're not having fun, you're going to be getting less loot because you're not going to want to be there and so will be less motivated to play the game in general. If you get twice as much loot and play the game a third as much you're not actually getting more loot. So if you think the jelly king is fun, don't go mess around with sewer stash, because playing the jelly king will still get you the orbs, or crowns or whatever you need.