AD&D consists of the following rulebooks:
Demon Idol makes references to all of these, though you don't need to own a copy of every one.
DMs at least need the PHB, DMG, and MM. The rest of the players can get by with just a PHB if they want to, but players desiring to master the system faster will no doubt quickly want for the DMG, since it contains the bulk of the rules.2) It contains rules modern gamers would expect to be in the PHB, like the combat rules and saving throw tables. 3) Demon Idol suggests using UA's magic item tables and spells, along with a couple other rules, but these are not required and you can always add them on later if you want. Your game will not suffer for their absence.
Additionally, while the bulk of DDG's content is a listing of example deities, its main value to your game is an expansion of the ability score tables in the beginning of the book. These detail the bonuses and effects of ability scores above 18, which are regularly invaluable. However, DDG is also one of the most expensive books to purchase – especially if you get a 1st or 2nd edition, since they contain the Cthulhu and Melnibonéan mythoi which were purged in later editions for “intellectual property” reasons.
If you want to buy a copy of one of the rulebooks, you basically have two choices:
The WotC reprints are decent quality and relatively inexpensive, so it's recommended to use their reprints at the table if you're concerned about putting table wear on the real deal. Note that the binding is glue so you don't want to stack anything on top of an open copy or you'll damage the spine and possibly loosen some pages – don't even nest another open book in one. WotC also sells PDFs of their reprints.
Earlier versions of WotC's reprints had some errors in them. Most of them appear to have been fixed by Summer 2022, though there are still some OCR errors. If you use the WotC reprints, you might want to check out the list of errors here and here, especially if your copies were from a while ago.