If you're being minimalist, you can play OAD&D with a PHB, a DM screen, & either a module or the MM. Or a PHB & a DMG.
Ideally, though, you should have at least a MM, a PHB, a DMG. The FF & MM2 & D&DG are good to have too. It's probably a good idea to be selective about using things from the UA. The unarmed combat bits there are much preferable to the DMG rules, but you can just wing it.
(I always liked MM2's create-your-own encounter chart stuff & its index that included monsters from the MM & FF.)
If you want NWPs, I'd probably just go with 2e rather than using the DSG & WSG.
I've never played a game that used the OA, so I can't speak to that.
The Dragon Magazine CD-ROM archive is invaluable. Also, drop by Dragonsfoot for downloads & discussion.
MM=Monster Manual
PHB=Players Handbook
DMG=Dungeon Masters Guide
FF=Fiend Folio
MM2=Monster Manual 2
UA=Unearthed Arcana
DSG=Dungeoneers Survival Guide
WSG=Wilderness Survival Guide
OA=Oriental Adventures
(As much fun as my OAD&D days were, I hated luging 6 hard bound books to each session. If I were to play OAD&D again, I probably stick as much as possible to the MM, PHB, & DMG. Or try to find those miniature versions that were published a few years back.

I really like my Basic & Expert D&D rulebooks. Thin & light.)