None. Rebreather and a certain fiend helmet apparently, cook-cook's i think.
Only certain 'quest' items are allowed with you, most of them worthless. Everything else is stripped from your character once you are taken to the Villa. You can only take what you find in Villa to the Sierra Madre. I suppose you could enter cheats if you had the PC version though.
Here's a tip to get descent armor into the Madre: In Freeside, outside the Silver Rush, there is a locked box next to the guard/Simon (you need 75 lockpick skill). Unlock it and there should be Van Graff Combat Armor. It will be a quest item if you didn't complete the Birds of a Feather quest.
Cheers, I'll try the armor for the quest