For this, what books and editions of them are the best?
From what I remember, there are no variations between printings of the books. Besides the Cthulhu Deities and Demigods. The content is all the same, only the covers are different. So whichever cover looks best to you, get that one. Or, if you have a PDF editor, buy whichever version you can and slap the cover you like on the PDF.
Stick with the core three for the rules and skip the other rules supplements. It will make things drastically easier to deal with. But pick up the other two monster books, MM2 and Fiend Folio.
What do I need to know when reading these?
No one ever actually play using all the rules printed in the books. No one. A lot of people online claim to have played all the RAW by the RAW, but I've never met an actual person in meat-space who's ever made that claim. Most people used the character races, classes, arms and equipment, and spells sections of the PHB but not much else. The absurd tables of weapon speed and weapon mods vs armor types were never used at any table I've ever heard about in meat-space.
People will inevitably bring up ADDICT and point to it as some kind of AD&D bible, it's not. It's a product of later players obsessed with RAW scouring every possible source to find every niche bizarre rule ever printed and smashing them all together. Again, literally no one played that way. When AD&D was new, D&D was still very much a folk tradition rather than an official RAW worshiping scene. It was only later that people began worshiping RAW. Actual AD&D players at the time when it was current used what made sense and ignored the rest.
It's worth noting the release order and dates of the core three books. MM 1977. PHB 1978. DMG 1979.
Year One you only had monsters. People used either OD&D or Holmes Basic for everything else.
Year Two you had monsters and PCs. People still had to use either OD&D or Holmes Basic for everything else.
Year Three you finally had all the rules. People forget that the to-hit charts are in the DMG...which wasn't released until two years after the MM and one year after the PHB.
What this resulted in is a lot...I mean a lot...of tables never really played AD&D RAW. They kept the bits and pieces of OD&D and Holmes Basic they used when the AD&D books were still being released. Early AD&D was a mishmash of game systems at the table. Groups kept using the rules they cobbled together, bringing in new players and teaching them their version of the game, those players went on to run their own games and either kept the cobbled D&D they were taught or modified it to suit their own tastes, and passed that on to their players. When a new book came out they'd look at it and decide what to use and what not to. There was no universal acceptance of whatever official stuff happened to be released. Most groups ignored everything besides the core three and the monster books, for example.
To make it even more confusing, most people didn't make the distinction between B/X, BECMI, and AD&D that we do today. It was all close enough to work together, so people used whatever they liked. For example, the version of AD&D my group still plays is a mishmash of AD&D, B/X, BECMI, 2E, and a bunch of house rules. We built the game we wanted to play based on what was available. What line it belonged to didn't matter. What edition was printed on the cover didn't matter.
Is it true that knowledge of how to play is passed on more as an oral tradition than through the books (a concept with which I’m familiar, given my Orthodox background)?
Absolutely. See above.
Any help from those who have played, are still playing, and/or loved it would be greatly appreciated.
Start with the absolute minimum you need to functionally play the game. Don't try to use all the rules in the book. You don't need most of it.