Equipment for Pure Gunner
I recently started playing as a pure gunner and need some help with my equipment. I'm using alchemers for my elemental and shadow guns, but have no idea what piercing gun I should go for. Also, would the Padded Armor family or Gunslinger Sash line be better? For the helmet I'm using the Masks of Seerus. Feel free to suggest better gear if anything I'm using here is bad. Your help is much appreciated.

If you're going for attack speed gunning, then I guess the Callahan will be your best option. I really don't recommend antiguas for gunners. You'll get carpal tunnel syndrome within 2 floors.
You might want to try charge spam gunning (which is what I like to do). If you're going to do that, then you'll want Mask of Seerus + Chaos Cloak. That'll open up the powerful Magnus charge, as well as the Autogun charges.
If you plan on eventually running a lot of Firestorm Citadel (which you will do whether you want to or not), then you'll need a Blitz Needle.

Have you read the Gunslinger Guide on the wiki? It's far from perfect, but it summarizes your options.
As others have said, alchemers have a high learning curve but high performance once you get skilled at them. Other guns with big charges are the magnuses (Iron Slug, Callahan, etc.) and the autoguns (Blitz Needle, etc.).
For armor advice considering reading the handgun section of my armor guide.

Armor
For armor I'd go padded armor + shadow + shock + gun damage low vs all with fire med+ as a UV if I were you. This gets you maxed out resistances against the things that are hardest and weaknesses to the things that don't matter as much- poison can be walked off and you'll probably get black kat set for freeze eventually anyway, even if you have to settle for 3/4* black kat.
A Piercing Handgun
You'll probably want a blitz needle for firestorm citadel, but if you're not there yet I wouldn't stress it. In fact, I'd really recommend iron slug- it starts out dealing piercing until 5*, and is a decent item for fighting fiends in conjunction with your elemental alchemer. When you eventually do get your iron slug built, you'll be able to team up with a team mate using a vortex bomb to speed-clear the vast majority of levels... which is really the dream in a nutshell.
@Tortoguns
I don't usually mention those to people.. not because they're bad or anything (quite the opposite, actually) but because by the time you're ready to go for one you already have the bulk of your gear made and really just want it for the sake of novelty. Of course, I'd really love to see a newer player actually go for one and report back to us how it goes. The optimal route (for newer players) is probably to get maskeraith and get carried through tortos by some leet player that wants to beat the tortos 200 times for fun and just needs your glyphs.
1) The Mask of Seerus is a fine gunner's helm. It pairs well with any of the elemental padded armors, Nameless, or Chaos.
2) Alchemers are fine guns that reward skill and practice. Good choice.
3) If you're a good switch shooter, it's hard to beat the damage output and stun potential of switch shooting a pair of Callahans, or even a Callahan paired with an Iron Slug.
4) If you're not a good switch shooter, a Blitz or a Gilded Griffin can do ok too. I used a Raptor for today's prestige mission.
5) A Blitz is still the preferred anti-Vana gun. It's also not bad against devilites, as the wide spread can negate their attempts to dodge.
6) Don't underestimate a Savage Tortofist with CTR+6. It probably shouldn't be your first piercing gun, though.