In his defense, there haven't been many recent threads about it.

UV
Not really important.
If you have ASI on your guns, then it will just mean that you won't need swiftstrike buckler and you can use a real defense shield.
If you have ASI on your guns, then you can prioritize a damage bonus armor set.
If you have CTR on your Blitz, then you can skip using Chaos for a different gun set.

So that said, you can make any of these sets without any UVs and you can be fine.

Shield: (ordered by usefulness)
Swiftstrike Buckler - (+3 ASI). Hopefully you won't need to actually stand in front of monsters much.

Grey Owlite or Dragonscale - Fire resist means you can sit in front of zombie fire breath, elemental defense will let you tank a Vanaduke mace hit or the fire balls/projectiles.

Armor: (ordered by bonuses)
Chaos set + Elite Trueshot + Elite Quickdraw (+6 DMG, + 2 ASI, +4 CTR) - Best bonuses, but fire will kill you. Only recommend this if you have good control over yourself. Gets Ultra (5) ASI with swiftstrike, max CTR if you have a level 10 gun.

Shadowsun set + Elite Trueshot + Elite Quickdraw (+6 DMG, + 2 ASI) - Max damage set with no drawback. Gets Ultra (5) ASI with swiftstrike, but no charge bonuses).

Justifier or Nameless set + Elite Trueshot x2 (+4 DMG, + 4 ASI) - Balanced sets. Gets max ASI with swiftstrike.

...I'd put down Deadshot but its bonuses only counts vs undead so it's not all that good in other situations.

Also, you can use a pet perk to push whatever stat you're "missing" up to max (so for example, if you go with Chaos set, gun ASI perk will give you max ASI/CTR/DMG; if you go with an ASI set, gun damage perk will give you max DMG/ASI)

Weapons: (ordered by my recommendation)
Nova Driver - Highest damage output alchemer for undead

Blitz Needle - Mainly use for Vanaduke, but its charge attack gives high piercing damage output that you can use to kill Trojans and Slag Guards.

Electron Vortex - Not a gun, but your teammates will love you for this. Works good with sword teammates and Neutralizer charge. The parts that takes the longest in a FSC run isn't the boss fight, but killing the monsters, and this will help kill large groups of monsters faster.

Neutralizer - Niche gun that you can use if someone has a vortex. If you get it, aim 1 charge on the right-most monster in a group and shoot immediately to make the shot blow up in the middle of a crowd, then repeat.

Storm Driver - useful... shock damage will hurt enemies that are in a big group and stop them from walking towards you. Shock status can stop Vanaduke from moving during his tackle move, but it's random.

Hail Driver - useful if you're a defensive player. If you freeze fire slimes, their fire will go out after 1 second, so you can hurt them with elemental guns. VS Vanaduke, you can use it in a pinch if you want some time to get water or walk behind him.

Valiance - Works on everything, but isn't the best at anything. If you don't go with Neutralizer, you can use this to kill slimes instead.

Sprites get the Swift Steps II ability somewhere in the 90s (might be earlier or later since they aren't in a fixed order)

A good gunner loadout for FSC would probably consist of shadow def mainly with a little elemental def mixed in there too. You'll also want fire resist, elemental and piercing guns (Callahan, Blitz Needle, Polaris etc...), and some ASI, MSI, CTR, and/or DMG increases.
Here's an examle loadout:
Armor=Chaos cloak
Helm=Black kat cowl or deadshot (or whichever one gives shadow def with undead dmg boost low) duster
Weps=Blitz Needle, Polaris, & Hail driver
Shield=Swiftstrike, any shield w shadow def, or any shield w fire resist
Trinkits=basically whatever you want.
BS perk=either gun ASI perk or Swift Steps
BS harness=elemental pierce or normal
Hope this helps :)