This guide attempts to highlight the different categories of 5* guns, what they are good for and who should use them. Keep in mind everything is relative and situational; exercise common sense when following any advice.
A note to newbies:
Spiral Knights has four types of damage: Normal, which is moderately effective on everything, and Elemental, Piercing and Shadow. These last three types each have two monster classes out of six that they are highly effective against (~50% more damage?), two they are highly ineffective against (~100% less damage?), and two they are neutral against. Therefore, in order to maximize the amount of damage you do, you should use a weapon dealing the appropriate type of damage against the monster you are fighting. Because the base damage of guns is low to begin with (the advantage is safety from distance), gunners should tailor their loadout to the level they are facing. Many levels spawn more than two classes of monsters, so it is recommended that gunners have at least 3 weapon slots. You can make do with two, but it is much harder even with the arsenal stations.
Elemental Alchemers:
These are the workhorses of a gunner's arsenal. Excellent damage against undead and constructs, team-compatible (they don't throw enemies around) and fairly easy to use. The recommendation is usually Nova Driver for extra damage, but Magma and Storm are fine too- just don't use them in places with Oilers or Quicksilvers. Hail Driver is less impressive, as gunner tactics usually involve kiting rather than freezing in place. They make passable sidearms for non-gunners because constructs (especially turrets) are what they often get used against. Unfortunately for beginning gunslingers, alchemers do not become particularly effective until the 4* Driver version, when bolts really start to ricochet.
Polaris:
This is the sidearm of choice for a swordsman. They are ideal for killing turrets at range- two of the three the turret types are weak to its elemental damage; strong enough hits will interrupt the turret's attack, and any non-shock turret has an additional chance of getting shocked, which can also interrupt their attack. Aside from attacking turrets though, the Polaris should be used sparingly as the knockback of expanded shots will annoy your team to no end. Having to dodge enemies bouncing around will also reduce the team's overall damage output. A pure gunner may consider taking one if they expect turret trouble, but I usually bring my Storm Driver anyway.
Biohazard/Umbra:
The only pure shadow guns. The Umbra Driver is generally the better pick especially if you can get medium or better CTR, particularly if you are looking for straight damage. As with all alchemers, the Shadowtech line doesn't really start shining until the 4* Driver. However, the Biohazard isn't a bad gun either, and has the bonus of herding and pinning gremlins against walls. The charged explosions are awesome-but-impractical, but still great fun nonetheless. If your only goal is to maximize damage, I would recommend Gran Faust or Acheron, but these guns are perfectly serviceable for dispatching slimes and the occasional gremlin.
Callahan:
The Callahan is the go-to pierce gun for Gunners, but I've found it rather lacklustre. However, there are no easy alternatives. Your best bet is to buff gun damage with Trueshot modules, so that you can knock down wolvers and devilites in full parties. While slow, it is a safe and surefire way to kill these enemies, as you can keep them safely knocked down at distance. Be warned that Alphas are difficult if impossible to knock down with a gun, so you'll have to keep kiting them. Unless you are a gunner, you will prefer a piercing bomb or sword, as the Callahan's damage output is rather mediocre.
Piercing Autoguns:
Blitz and Plague Needle are powerful situational weapons. They are famous for dealing with Vanaduke, but are also fantastic against Trojans and Alphas. Blitz is the recommendation, as the increased damage still outperforms the poison effect. The only benefit to Plague needle is that it weakens monsters, causing them to do less damage to you. The primary draw of these guns is the charge attack which roots you in place for some time, so they require much more skill to use- a missed attack generally means getting hit hard.
Normal Damage:
You won't see any pure gunners carrying normal damage weapons, because they need all the damage boosts they can get. That said, there are some normal damage weapons that see a bit of use. In particular, the Valiance is an acceptable sidearm for the nongunner because of its generality; if you don't expect to be facing turrets and want an all-purpose gun, this is your weapon of choice. The Volcanic Pepperbox is also amusing to use, although like all Autogun lines, the charge attack really hampers mobility. The Supernova and Neutralizer are not recommended because they have few or none of the advantages their counterparts offer, and all or most of the drawbacks. The same is true of the Iron Slug, but even more so.
Split Damage:
The much-maligned Argent Peacemaker and Sentenza are not general-purpose weapons as their split types might suggest, but specialized weapons. Again, no pure gunner should use these weapons barring exceptional circumstances (Peacemaker might be acceptable in FSC; Sentenza might have its uses in Deconstruction zones). They make passable albeit subpar sidearms for non-gunners, again due to the way split damage works. Personally, I am against changing them to pure-typed, because I have always like the theming behind these weapons. They could use higher base damage and a bonus against the types they are themed against (Undead/Fiend for Peacemaker; Beast/Gremlin for Sentenza).
Mohandar, I like it. I have two minor suggestions.
A lot of new-intermediate players (your target audience) don't understand damage types. So maybe add a note at the start, explaining why a gunner wants three slots, and why he should fill them with piercing, elemental, and shadow (or utility sword?).
You could clarify: Why exactly is Polaris better than Nova Driver or Storm Driver against turrets? Because Nova lacks shock, and Storm does less damage?