For the past month, I've been carrying around a Blitz Needle. Individual shots are pretty weak, but they are really handy for Silkwings and Greavers, especially when you have the luxury of distance to ready your shot. You can't move around while shooting, which is why I have started to appreciate the Antigua, and I look forward to expanding into that line.

I haven't tried the others you mentioned, but they are each described on the SK Wiki: http://wiki.spiralknights.com/Handgun

Which gun you consider 'best' depends highly on your play style, and also on what you're facing, how many weapon slots you have, etc.

1) No single gun is "best", but I like the Silversix line and Voltech alchemer line. The former is great in the FSC and undead, with its mobility making up for mediocre damage everywhere else (also makes a great weedwhacker and mining tool); the latter is good in general against constructs AND undead, the enemies that you are most likely to want to gun down at range. The Firo and Cryo lines are also all right. I run with two swords and a gun as a fallback; I eventually hope to add a shivermist/ash to my arsenal.
2) This is indeed explained in depth in the wiki
3) The Valiance is so-so. It's not a bad gun, but it has no status effects, and doesn't yield bonuses against constructs and undead. You could argue that it has no weaknesses, but that shouldn't come into play (stuff that resists piercing and elemental are usually most easily dealt with by sword anyway).

On a side note, if you do decide to run with a Voltech, holster it when you encounter quicksilvers (the metallic slimes). If you've ever been to a Thunderfist: Slimey Showdown in T3, you'll know why.

Sorry for the double post. Forgot one thing.

Valiance. The damage on it is ok if you aren't packing a bunch of damage types and are used to constantly exploiting monster weaknesses. Still has 3 to 4 rounds per combo, you can move while shooting/reloading which is nice, but the main benefit to the valiance over the other 5 star firearms, and the big difference between it and the master blaster, is that each hit pushes the monster back a tiny bit. It's the only handgun that does knockback on a regular hit, and can be very useful for this reason, but the damage on it is much less than what you'd get from an Iron Slug, and it can't inflict statuses like the pepperbox or alchemers.

The Blitz Needle has a longer range than the Callahan (by far). The Callahan doesn't stun you unless you use the charge attack.

Standing still while shooting is far worse with the autoguns than with the magnus guns. Autoguns fire a round of shots, then reload. Magnus fires just one shot, then reloads.

Why do you say the charge shot on the Blitz is useless? Personally what annoys me about autoguns (well, one feature that annoys me, among many) is that not only you stand still while firing, you can't turn around either. So you're firing your entire clip in one direction. This just gets magnified with the charged shots, since you fire even more bullets, standing still longer. The Pepperbox compensates for this by dragging monsters into the stream (if you hit them), the Blitz doesn't.

You haven't tried 3 out of 4 of the weapons the OP asked about. My conclusion remains: try a weapon yourself. It's the only way to get accurate information (at least until we get damage numbers in the wiki).

I currently have the following 5* guns in my arsenal. They're in the order of usefulness in my opinion:

Callahan, Hail Driver, Argent Peacemaker, Valiance, Umbra Driver, Volcanic Pepperbox, Iron Slug

The first four are very solid weapons.

The Callahan is great for three reasons. The most annoying enemies to engage with a gun (wolvers and devilites) can't move fast enough to dodge the shots. They're knocked "up" about half the time, and take major damage from it. It is also great in "limited engagement" situations, where you're spending most of your time repositioning and not actively attacking (Trojans, Vanaduke, etc) since it lets you pack the maximum damage in the shortest engagement time. Argent peacemaker is higher DPS when you can just unload to your heart's content, but it requires you to be actively firing for a larger percentage of the time. Since a lot of fights call for repositioning with intermittent firing opportunities, the Callahan is better. The thing is amazing when it comes to dropping Trojans and will let you do a lot more damage than any other gun. It's also amazing for sniping silk wings out of large groups.

The Hail Driver used to be my favorite before I fell in love with the Callahan. Freezing enemies in place can be the difference between life and death, especially when fighting oilers on tier 3. It also does very respectable damage, particularly if you know how to shoot into pockets so all the ricochets hit. Single target the damage doesn't seem great, but when you remember that every shot can hit 3 times, this gun is very good at mowing down large groups of enemies, and keeping them frozen and out of the way while you do it. If the shivermist weren't so common these days (and so much better at locking enemies down) this gun would probably be #1. Storm Driver is also right about here in terms of usefulness. I leveled up and sold three of them, so even though I don't carry one currently I feel confident judging it and placing it tied at #2.

The Argent Peacemaker is just a damn good gun. The split damage means it's rather well rounded and while the DPS on most enemies isn't spectacular, when it comes to fiends and undead (which are weak/normal to its two damage types) it is the highest DPS gun in game. It boasts the longest range as well. I rank it third because of its spammy nature (I prefer two, carefully placed and devastating shots to six "plinks"), the fact that you move slower while firing than with an alchemer, the fact that you have to be able to fire consistently to get that high DPS (again, spammy), and it's lack of utility (stun, knock up, knock back, freeze/shock/fire, etc).

The Valiance is a great gun for three reasons. If you're a total gunner you'll want it because it does normal damage reliably at a distance without immobilizing you like the Volcanic Pepperbox or the Iron Slug (which is the worst 5* gun in game, more on this later). This is necessary for the mask phases on the vanaduke fight. As "water boy" I can throw a water droplet, extinguish the mask, fire six high damaging shots, grab the next water droplet, and extinguish the mask immediately. I can completely dominate the mask while still doing damage and allowing my team to just stand next to the thing and cut it apart. This makes these phases a joke (provided I don't miss). It is also the only gun in game with knock back. Very useful if you find yourself with your back to the wall and no sword to cut a path to freedom. The other reason you might take this gun is if you only carry one gun and just want a solid, well rounded gun. It's on par with the peacemaker, considerably easier to get, and offers a bit more flexibility/utility for situations outside of vanaduke/graveyards/fiend levels.

On to the weaker guns...

The Umbra Driver is kind of medicore. The enemies that are weak to it will die faster, but there's a problem there. Gremlins dodge like crazy and killing them faster isn't always the most important thing. Once upon a time this gun knocked enemies down making it useful. Now that it doesn't it has lost its appeal. I tend to use my Callahan on Gremlin healers to do good damage while, more importantly, interrupting their heals with its knockdown. Yes, the umbra driver kills jellies faster, but they're typically so weak that the only time I care about how fast they die tends to be on T3 oilers. Even then I want to freeze them with my hail driver rather than DPSing them as hard as I can to make sure I don't get lit up like a christmas tree. The overly nerfed this gun. No two ways about it. Still decent, but not as useful as it was.

The Volcanic Pepperbox is a decent gun. It's charge attack is one of the most damaging attacks in game and it lights things on fire. But it makes you extremely vulnerable and it is hard to take full advantage of its DPS since you have to be pretty much point blank. The main reason I pull this thing out is for the "tractor beam" effect on its charge shot which for some reason pulls enemies towards you. I also use this when I'm feeling exceptionally lazy and I'm just running around behind three bloodthirsty swordsman. In any serious situation this gun tends to get me killed while doing mediocre damage.

The Iron Slug is a joke. It takes all the disadvantages of a Magnus with none of the advantages. It loses its ability to stun on normal shots, it loses specialized damage to give it niche appeal, and does not have significantly higher damage to compensate. Yes, normal damage is nice sometimes, but the only times you'd want to use it over a Callahan would be constructs, jellies, and Vanaduke's mask. In all three scenarios you're much better off using a Valiance since this gun still forces you to stand still, does mediocre damage, and has zero redeeming qualities.

The Valiance fires three shots before reloading. It sometimes looks like four because of some weird bug.

I use it as my main gun, but that's because my other slots are taken up two swords and a bomb. If you plan two carry two or more guns, it's better to specialize so you can take advantage of damage weaknesses.

I only have the Pepperbox and it looks like there's some slight differences between it and the Volcanic buuuut I think I can still comment on it and perhaps the Blitz Needle.

You got to think of the Autoguns as lances or really long Troika style swords. The charged attack does incredible damage but will get you murdered if you use it at the wrong time, normal attacks risky as well but much less so. It might seem as if Autoguns are stupidly risky since they leave the user open and can't get the user out of terrible situations like some charged sword attacks can but if the Autogun user is good enough they can stay safe while dishing out huge damage.

I'm only in Tier 2 but it seems to me like Autoguns have a very fun high risk/high reward play style.

Once you learn how many bursts it takes to down an enemy you know when it's safe to just unload on them when they're in melee range and charging an attack.