So I haven't had much experience playing Kat since her rework and I really just don't know what items to try and build on her first.

I know Sorc boots are standard early game, but would I try and go for Abyssal Scepter, Death Cap, or DFG as my first item? I'm just unsure...

Thanks!

I usually go sorc boots scepter death cap DFG void staff

When I play Kat my first item is useually the Hextech Revolver, mostly for the spellvamp sustain. Afterwards it's useually a Liandry's.

I useually get Liandry's for the spell pen and extra damage and get the Ninja Tabi boots and Abyssal Scepter for some defense.

The full build is:

Hextech Gunblade
Liandry's
Ninja Tabi
Ab Scepter
Deathcap
Zhonya's Hourglass

My personal build is

Boots+3 Pots>Sorc. Shoes> Guise> Abyssal>Rabs>Liandrys> Hourglass> Voidstaff.

Why Gunblade by the way? The AD doesn't really help much for the W and I think it's not that worth it for the ultimate. And isn't the spell vamp ratio really low for AOE spells?
I know Katarina really needs sustain but I don't see the usefulness of gunblade.

Kata doesnt need a gunblade. Better if you rush Sorc Boots or Merc Boots, then judge if you need MR or Armor and build either Abysall Scept or a Chain Vest into Zhyonas Hourglass. Then get a DFG if your facing tanky bruisers and/or Deathcap. Finish off with guardian angel.

Is hextech all that bad though? I mean wouldn't the sustain help?

Well it isn't all the bad, though people could make a case for getting the will of the ancients with your revolver instead. I used to get the gunblade and never took it off the list. The lifesteal is useful in marginal cases I think. The ranged slow is nice. The AD isn't as useful as it used to be, but that doesn't make the item useless either.