Hmmm.
Well, This is what I think, is good.

Shadowsun Stetson + Chaos Cloak

2 Penta Heart Pendants If you have trinket slots
Sprite perk: Gun ASI Increase ??? (If you don't have this you can just use the fire resistance perk cause it helps alot)
Swiftstrike Buckler or Grey Owlite Shield Or Crest of Almire

Weapons:
Argent Peacemaker (Undead Max x ASI FTFSC)
Blitz Needle
Storm Driver
Polaris?

I hope this helps! :D

~Tech-Knight-Die

EDIT: Damn I just realized What I wrote here was FSC loadout rather than just the OP. Meh It's okay I'll leave this here

It depends on what you wanna do and what your weapons are.

First off, I'm gonna assume you only have 2 weapon slots and you're not interested in getting additional slots. I'm also going to assume you'll be playing on Elite with a full party.

Since you're focusing on wanting to kill Zombies, I'm going to assume that you're not that interested in taking on Vana either. I know a lot of players who only want to do up to the 4th level, then avoid Vana. Back in the day when Energy was a factor, that's a serious consideration.

It also depends on whether or not you want to have Blitz Needle. Again, I'm going to assume you don't want Blitz Needle. Why? Because the DPS on Blitz Needle and the required play style for Blitz Needle are such that additional damage from Abilities is kind of pointless. Blitz is all about baiting and dodging and positioning etc. Blitz is all about the Charged attack, so ASI's mostly pointless. Then it's a matter of whether or not you want to Blitz from a distance or at point blank range. For the former, extra Damage is again, mostly pointless, while for the latter... you might want additional damage if you're playing on Elite + you have a full party. At anything less than Elite or less than 3 players, you probably don't have to worry about DPS much. If you're shooting something at point blank range, it's going to OHKO it.

Okay, those assumptions aside now. If you're only going to be dealing with up to level 4 of FSC, and you want to be able to tank shots from Slags/Zombies, then of course, I'd recommend either the Shadowsun or Deadshot sets, or a mixture of both. However, while you would take low damage from their hits, the problem with FSC is the Fire status. If you're not resistant to Fire, then even a single lucky shot from a Slag might be enough to kill you, or reduce you to very near death.

So what I'd recommend would actually be 1 piece of Shadowsun/Deadshot and another 1 piece of Volcanic Demo/Divine Mantle/Grey Feather. The reason is that the latter would provide you with some measure of Fire resistance. Divine and Grey Feather would also provide you with some Shock resistance, which is an uncommon but not rare status in FSC.

It's not a conventional setup, but it's a combo that I've used myself.

The thing is though, unless you're a Blitzer, you really don't need any special armor as a gunner. If you're a Blitzer on Elite with a full party, you might need Damage bonuses to make sure you can OHKO Trojans, but if you're only packing an AP, Polaris, Storm Driver etc, no one expects you to kill anything yourself.

Your best defense is a good dodge-sense. So your setup should simply be an insurance policy rather than the crux of your gunner.

If you usually grind Vanaduke, Deadshot+Shadowsun is a better set than full Shadowsun. But Undead are just one of the six monster families. Shadowsun is a better choice in Arcade where the monster family is different on each level.
If you choose Deadshot+Shadowsun and bring a sidearm (a bomb or a sword), that sidearm will have Undead Med bonus too. Example: 4 weapon slots-Nova Driver, Storm Driver, BaB, CIV. All these weapons will have the undead bonus applied (Nova, Storm, BaB-undead med; CIV-undead ultra because it has natural Undead High bonus).
Full Deadshot set is for hybrids.

I don't have data on Plague Needle with damage bonuses, but each level of damage bonus adds roughly 5% to observable damage (data). Working on that rule of thumb, Plague Needle with damage+4 would do about 241 damage per charge bullet, whereas Blitz Needle does 272 damage per charge bullet (depth 28, against fiends and beasts). These numbers ignore poison, but my guess is that Blitz+0 out-damages Plague+4 against Vanaduke.

Going to be blatantly suggest the copy paste build since you said you played FSC so many times. Just go full chaos + swiftstrike + ASI/Damage trinket + msi: med perks from battle sprite. Those gears would get you max damage, max ctr (with level 10 weapon), and ultra asi regardless weapon uv on handguns. MSI is life safer sometimes... when you charge blitz. Certain amount of damage bonus is required to one hit Trojan for your own convenience (I believe you need max damage bonus to one shot blitz trojan at 3 party member elite difficulty, also you need max damage to one shot blitz zombie at full party elite mode).
0 fire resistance and negative fire resistance actually doesn't differ that much, both has 9 sec duration, but negative will hurt you 1 - 2 health bars per tick.
Based on my own experience, sword user should be the safest one to prevent any damage though. Being a gunner doesn't mean that you should always keep distance. The main point of not getting damage is by trying to read all monsters' movements regardless your class (swordman, gunner or bomber) then avoid them. You should be spamming charge (generally on common weapons) for easier monster controls.
ASI still helps to recover faster after blitz charge, though just a bit significant different.

Oh and feel free to friend me, I would gladly accompany you through FSC if you're wondering about my play style based on these.