I'm just starting out, and I noticed that I can only have two of either guns, swords, or bombs. Correct me if I'm wrong, but (for PvE at least), I get the impression that gun+bomb is the best setup. This way you can keep everything at a distance, and you get an area attack from bombs. Is there a reason I should throw a melee weapon in that I'm not seeing? If so, what should come out, guns or bombs? Thanks.
swords, guns, bombs (for a newbie)
Your question is quite reasonable. As Bluencool says, you can actually carry up to four weapons, which give you more flexibility than just two. I myself use three.
Before you get much farther in the game, read the wiki page "Damage", and learn the monsters' vulnerabilities and resistances. Then you may find yourself considering other play styles, such as
* two swords of differing non-normal damage types,
* two handguns of differing non-normal damage types,
* one sword and one handgun of differing non-normal damage types.
Generally, there are a few different factors to choosing a weapon. But keep in mind- once you get to two-star and three-star weaponry, you should plan your gear around reaching five-star weaponry. Many two-star and three-star weapons will upgrade into five-star weapons through Alchemy, but some don't; avoid making the Cautery Sword and Wrench Wand, and the Spur isn't that great either.
The Normal-damage weapons aren't terrible crap as Bopp implies. Troika can be upgraded into the Sudaruska, which, while difficult to master, has a very powerful charge attack (and is just flat out fun to use in general), and Calibur is a good all-rounder. Blaster is a good sidearm. And the Blast Bomb becomes the Nitronome, which is a great bomb if you're careful with it (it has high knockback, so be careful you don't blast a Mecha Knight into a party member). This is not to say the specialized damage (Piercing, Elemental, and Shadow) weapons are bad choices by any means; they are also generally good.
As far as your original question goes, well, there are vast differences between different types of Swords, Guns, and Bombs. I recommend you read these:
The wiki's Bombing Guide
The wiki's Gunslinger Guide
The wiki's Swordmaster Guide
These articles all have detailed information on each type of weapon in the game.
it's all about play style and personal preferences. the one thing about bombing is that it can be challenging to solo, whereas the other two "classes" can easily solo anything. many knights often go swords because dps is high and the learning curve is nice and easy. my personal arsenal includes nearly 10 5* of bombs, guns and swords, and i'd have to say i enjoy gunning the most. playing as bomber for a full team is also rewarding in its own way.
since you just started, experiment! playing with different weapons now is low in cost and the enemies wont hit as hard as they do in t3. go to the auction house and you can purchase many swords, guns and bombs for 1k cr a piece. find something you truly like and plan your first 5* set out carefully. once you get to vana, the money is easier to make and you can make a bunch of random silly crap like i did :P
if you wanna stick with gun/bomb, i'd recommend either pulsar or antigua lines /haze (voltaic tempest or ash of agni). i think overall this setup is going to have pretty low DPS but it is a cautious set up that can easily make things safe. more exotically, you can go autogun/vortex. both of these set ups ironically are optimized by the full-offensive chaos set.
gun plus bomb setup doesnt give you that huge dmg output, so consider using a sword along with one of those. Get all damage types, and youll be good to go.
-you can have every single weapon in the game. if you mean equipping, you have 2 free slots and 2 locked slots. those slots can be unlocked by buying wep slot upgrade from supply depot for 200 ce -crystal energy-. the upgrade lasts for 1 month. you don't need any weapon slots for now.
-there are many different types of swords, guns, bombs and enemies and all enemies have a different strategy to use against. some bombs focus on status effects rather than damage, some guns have AoE, some monsters dodge bullets. but if you choose the right weapons against right enemies, any combination will do fine, regardless of weapon types.