The relevant material is the five classic (i.e., through 1990s) editions of D&D, and AD&D. Some of the books include
- basic/etc. D&D rules (five editions... ToME has some classes missing)
- AD&D rules (two editions, some classes missing, and schools of magic you don't have yet)
- AD&D Oriental Adventures
- basic D&D Gazeteers (GAZ)
- basic D&D Creature Crucible (CC) series
- AD&D 1st ed. Dungeon Masters Guide has dungeon generation tables optional rule system (would make for some dungeon variation)
- AD&D 2nd ed. Complete Handbooks series (titled for races, classes)
- AD&D 2nd ed. additional/optional rules (Dungeon Masters Option, Players Option) may have other stuff
Some classes missing include D&D monk (also in AD&D) or mystic, several GAZ ones, and AD&D assassin, barbarian, ninja (and others in Oriental Adventures.) Of course GAZ books are set on the Mystara world, and there are many AD&D worlds that may have material that is otherwise generic if removed from setting. I have all the generic books and some that are in settings, or know people who have the rest, so I can look stuff on request.
The way they are backwards-compatible is you can play classes any of the five classic (through 1990s) editions of D&D in AD&D, and any of both in AD&D 2nd ed. or the version with its optional rules. Various D&D had monks and mystics (similar) in different editions, but you could use the one from older editions in newer editions. You could use most the numbers for elves, for example, apart from ones necessary for the edition such as armour class, and have two or more types of elves, one that progressed faster to do well for fighting, and another that progressed better for magic. AD&D 1st ed. had assassions, and 2nd ed. didn't unless you still had the 1st ed. books and decided to include them, and 2nd ed. had other classes you could use with a more 1st ed.-type campaign if done right, etc. There's at least one detailed article on all this compatibility that I can find if you're interested.