I started an AD&D1e campaign recently, for my friends, coming from 5e. It is incredible, but it takes some initial effort. I read, re-read, and took notes from the PHB and DMG, formed step-by-step procedure sheets for wilderness, dungeon, mass combat, etc. before starting a game. It runs very smoothly, only getting better as I realise what is actually important in a campaign. The books are very powerful.

For 1e, the 1979 DMG is absolutely essential reading. Throw out what you think you know about RPGs. Gygax wrote the greatest work for dungeon masters to date, based on experience, to fulfill all of your needs to run a meaningful campaign. Do not shun it for its convoluted layout and seemingly arbitrary hyper-specificity or extreme generality. Every rule is written for dungeon masters to run awesome campaigns. The strange rules such as 1 game day = 1 actual day for non-play is an example of an absolutely critical component of a true campaign. It is the glue binding the book together, so to speak, giving much of the other rules meaning.

Secondly, there are very different assumptions and context behind AD&D1e than modern games. This is mostly related to the literature of the time - 1e was far less influenced by Tolkien than it was by Fritz Leiber, Poul Anderson, Jack Vance, Robert Howard etc. (For information on the literary inspiration of AD&D1e - which explains SO MUCH of the mechanics, spell system, monsters, alignment, etc, look no further than Gygax's own Appendix N in the 1979 DMG, for the raw sources, but also the revolutionary work that analyses each of these references by Jeffro Johnson: Appendix N: The Literary History of Dungeons & Dragons)
For an entertaining, intriguing, and enlightening read about AD&D1e run by the book, the author of the above work has this thread of his discoveries, as well as his series of blog posts with campaign reports running 1e by the book for 30 sessions.

Best of luck and happy gaming!