For Tier 2? I would pick a Magnus or an Alchemer.

Magnus' shots travel fast enough to hit (and knock down) enemies that auto-dodge bullets such as Wolvers, Devilites and Gremlins. The problem is, you only get up to two shots per combo, and you can't move while shooting or reloading.

I remember hearing someone recommend an Alchemer paired with the Flourish series of swords. Wolvers and Devilites will auto-dodge bullets, but are weak against Piercing-- which the Flourish provides. Since the troublesome auto-dodging Beasts and Gremlins resist Elemental anyway, you may as well make that your gun's damage type. (Don't worry too much about the slow bullet speed, they travel faster and can ricochet off targets and walls in the upgraded versions.) Alchemers also only get two shots per combo, but you can move while shooting and reloading.

I like the Cryotech to keep the enemy off me, and so I don't have to worry about Oilers or Quicksilvers; Firotech is good for putting out pure damage via lingering afterburn; Voltech has a trade-off between status-based damage and restricting the enemy's attacks. Prismatech and Shadowtech don't have status effects attached; Prismatech they deal a tiny bit more damage to compensate. (But I still think I'd rather have a status-based Alchemer.)

Try the charged attack on the Autogun. You don't have to move, the bullets will actually pull the enemy to YOU. Just be careful not to try this if the enemy was winding up to clobber you.

(This also works for the Pepperbox series but not the Needle Shot series.)

among the alchemer guns,

shadow is not the same as cryo, firo or volt
shadow is good for slimes and gremlins..

cryo firo and volt (and prisma but lets leave it out) does elemental damage
good for undead, and constructs (those tree monsters and robots)

http://wiki.spiralknights.com/Damage

with those 2 guns, you are good enough to cover much of the monsters,
unless you run into beast(wolvers, chameleons) or fiend(those little devils)
they are tough to hit, but they take normal damage from either of the 2 kind of damages

one thing you have to consider with cryo firo and volt alchemers is that they do status damages
lets start with cryo, its one of my favorite effects.

Cryo freezes enemies in place. And if you or the other enemies do not land an attack on the frozen enemy,
the frozen enemy will take huge damage after the freezing fades.
the problem is that when you are spamming shots, your first shot may freeze the opponent and your second shot may unfreeze it,
leading to freeze doing not damage at all.
even if you are careful, other free enemies may accidentally unfreeze its friends =p

Volt causes shock, which is unclear to me. it seems to cause damage when the enemy moves, i was expecting it to stop the enemies from dodging,
but i have not seen that happen.

Firo is good for spamming, Firo causes fire, which does damage overtime and cannot be stopped like freeze,
fire causes damage more often the shock.

Thats a cursory view over my 4 preferred alchemers.
I can get by with just shadow and firo(slowly..), but if i had to choose only one gun,
I recommend the Blaster.

It does normal damage, which means it will deal damage to all monsters.
its fast enough to hit monsters that dodge.. enough..
which means you just take longer to kill them.
it has a 3 shot combo, so you can shoot twice, stop and skip reloading.
most importantly, you can walk while you shoot

A fully leveled Blaster kills most T2 enemies in 5 to 10 shots. IT IS WIN.
Plus, it deals the same amount of damage to all monsters. From my experience, Jellies and Kats take 5 shots, Gun Puppies, Chromalisks, and Scuttlebots take 6, Wolvers take 7, and Lumbers and Retrodes take 10. not sure about the other enemies, haven't seen much of them atm.

You can check "Ask a Master Gunslinger Anything" guide.
Also this post by Original Gunslinger may be useful.

My personal choice is Magnus + Voltech Alchemer.
If you're going to use handgun as backup weapon only I'd advice Alchemer or Blaster.

Magnus is best for piercing damage, Shadowtech is best for shadow damage. You'd be better off with a sword than with an autogun.

Guns are so underpowered that I've all but given up on the gunslinger route. I run with a Silversix, and although the damage output is mediocre on everything but undead, the rapid fire and mobility makes it suitable against slower constructs like gun puppies, lumbers and retrodes. I still prefer to sword them when I can, but when I want to play it safe or have no option (i.e. gun puppy across a gap), the Silversix has never let me down. The large clip means you don't need to be as precise about counting shots. For an alchemer, shot-pause-shot-pause is crucial if you are in a situation where you need to shield in a hurry, and if you accidentally squeeze off that extra shot (whether due to lag or miscounting) the reload animation leaves you painfully vulnerable.

Silversix is by no means optimal, but it suits my style better than the blaster series. I'd love to try the Cryotech alchemer series at 4*, but probably won't get to do so in the near future due to expense. I will say though, the Silversix doubles as a great weedwhacker and mining implement. =P