These are my notes on D&D as first released in 1974, and doesn't discuss variants that came later as it evolved, but is related to my experience with the game.
The beginning of Dungeons & Dragons are war gaming rules published in The Courier magazine by Leonard Patt, and played by the New England Wargamers Association (NEWA). This led to a rewrite by Gary Gygax that became Chainmail. The connection with the Panzerfaust fanzine, and the Domesday Book, with Patt's Middle Earth rules as preliminaries, is explained in The Making of Original Dungeons & Dragons[H24], and Peterson's Playing at the World[JP24]. Gygax also wrote the Fantasy Supplement to Chainmail.
D&D proper begins with a follow up to the Fantasy Supplement written by Dave Arneson. This follow up used Arenson's Black Moors medieval setting. Gygax continued to adapt the follow up with feedback from Arneson and this became the formal Dungeons & Dragons. The company Tactical Studies Rules, Inc. (TSR) was formed to promote Chainmail, and produce it, the supplements, and other games. The third edition of Chainmail was reprinted seven times (eight printings), each with relatively minor corrections. For D&D, it was reformed as TSR Hobbies.
The original D&D was printed as three manuals, the equivalent to the player's handbook first, then a guide of monsters and treasure, and finally a guide for traversing the dungeon and outside the dungeon. The first two printings came in a wood box (the third and after being in a white cardboard box) with the three manuals and enough room for a third edition pamphlet of Chainmail to be added. Thus, D&D should be thought of as a replacement to the Fantasy Supplement, though it is no longer Chainmail being played. This mostly used the dice system we are familiar with in pairs, especially several 6-sided traditional dice, sans d20 and percentile dice (the d20 acting as d10, two of which could be used for percentile throws), and the game Outdoor Survival, manufactured by Avalon Hill (now part of Hasbro Games), for on-ground terrain traversal (especially the hex map). Outdoor Survival can be useful for concepts of out-of-dungeon play for the DM to imagine what to invent.
The Alternative Combat System, starting on page 20 of Men & Magic allows one to play using D&D specific rules. It might be worth noting some of Gygax's 1975 explanation of D&D in the Europa fanzine, and clarifications published in the first two volumes of The Strategic Review, if deciding to actually play D&D in this century. However, Chainmail is still necessary as a reference to understand implications from the alternative system. The sequential man-to-man play can be tedious and drawn out if following the rules as written (RAW), without any of the modifications from the supplements. D&D is still a Chainmail wargamer's game, though as Gygax clarified, an adventure game not wargaming.
Four supplements extended and modified the rules and concepts until D&D was able to be played independent of the Chainmail rules. The final supplement gave instructions on how to play 1:10 armies against each other, completing D&D's independence from Chainmail and formerly succeeding it.
The Great Kingdom is the original game setting, Blackmoor being to the North, and castle Greyhawk and its city to the South, but there was no restriction requiring the use of the Great Kingdom. Scenes in Earth dungeons or landscapes as a medieval game was anticipated. The rules typically required a larger amount of players compared to today (4-20).
The Original Dungeons & Dragons Premium Reprint Edition released in 2013 by Wizards of the Coast is the quintessential box set edition of D&D. It does not include Chainmail, Outdoor Survival (or any accessory map), nor Swords & Spells. The 50th anniversary book The Making of Dungeons & Dragons[H24] gives a documented game history, includes the first printings of the three game manuals, and the first three supplements. It also has descriptions of Chainmail (second edition) and Outdoor Survival.
It is to be observed that those who play D&D are a large community, with different styles of playing and running a campaign. It's natural that rule interpretation and play styles will evolve. I see supplements, modules, and all of that as a kind of report of these interpretations and styles, which then influence how others play the game. It is inevitable that at some point this will evolve into a new game based on what has come before. This is what happened with the Holmes Basic Set, and Advanced Dungeons & Dragons, which replaced the old, more open style of play. An adventure gaming industry was spawned by the original game. TSR Hobbies did not restrict itself to D&D either, authoring other games, inspired by the first, especially those in the tabletop adventuring gaming format it had invented, generating an industry that was ultimately called tabletop role play gaming (TTRPG). At the same time I don't think this justifies burying publication of the original game for the new, or stopping play of older games. There are those who still play D&D fifty years later. Even Gygax continued to do so in the last years of his life. Find the game you like and play it with those you like to play it with. Be open to learning different, or at least new, editions, and other TTRPG systems, as time and interest allow.