It really depends on how much of a purist you are.
If I’m going to watch the originals, I still prefer the Despecialized Editions. They may be stuck at 720p, but for the most part they look cleaner and sharper than 4K77 and 4K83 because they’re sourced primarily from the original negatives. These are reconstructions though, and occasionally seams can be seen, particularly when Harmy had to rely on upscaled Laserdisc-quality footage. When Harmy eventually creates new versions using 4k sources, they will arguably be the definitive way to watch the OOT, but that’s a ways off.
If you want to see versions of these movies that are completely untampered with, 4k77 and 4k83 are the way to go, since they are actual scans of original film prints, with no SE sourced footage. They do look a little “rougher” and less finely detailed, but not moreso than the films would have looked during their theatrical run.
As for fanedits, I think there are two for the OT worth pointing out: adywan’s Star Wars Revisited and Hal9000’s custom special editions. These edits are primarily for people who admired what the SEs were trying to do, but disagree with some of the actual decisions that were made. Hal9000’s edits are basically hybridizations of the original and SE versions of the films and revert some of the more controversial changes. Currently ANH and ESB are available in full quality and ROTJ is available as a workprint. The Revisited edits are much more ambitious and essentially seek to update the films’ visual effects across the board to a more modern standard, as well as fix various continuity errors. Currently ESB is available in HD quality, and ANH is available in DVD quality only. An HD version of A New Hope is forthcoming, as well as an edit of ROTJ.