I would suggest 4K77 and 4K83 for SW and ROTJ. Highest resolution (whether at 4K or 1080p) that the OUT is available in, and they are authentic scans of original 35mm prints — not a single frame has been altered, as they all come from long before the SE ever existed. You know you’re seeing it as close to the original theatrical experience as possible when you watch them.
That said, they do have a decent amount of grain (especially 4K77) which may bother some people. There are versions with the grain digitally reduced (DNR), though. Empire (4K80) is not finished yet however, so if you want consistency across the trilogy you may still want to look at Despecialized.
Other advantage to Despecialized is that most of it is sourced from the Blu-ray, which means that it is closer to the original camera negative — it is therefore in some respects clearer and cleaner with less generation loss compared to film prints. However, it is currently stuck at 720p, parts of it are sourced from the GOUT which had to be upscaled, some of the digitally recomposited shots from the Special Edition remain, and the Blu-ray itself has a host of problems that had to be corrected as well as possible (not the least of which is color). The result is a stitched together product that is very well done but might bother purists in some ways. Still, for Empire at least it’s the best option. The only complete 35mm scan of Empire that’s been released is the unrestored Grindhouse, which is interesting from a historical perspective but rough to actually watch due to all kinds of issues with damage, color, and noise.
Puggo versions are sourced from 16mm, and they are likewise interesting historically but not what I would choose as my main version of the trilogy.
The GOUT is an early 90s Laserdisc master that was unceremoniously slapped onto DVD. It looks only marginally better than actual Laserdiscs, if that, and is not even anamorphic for widescreen TV. Which was standard even back in 2006 when it was released. Definitely not worth your money tracking down in this day and age IMO. In fact I actually prefer the older Laserdiscs from the 80s and early 90s (before the “THX Certified” releases), such as the Japanese Special Collection, because I like their color better. I wouldn’t bother dealing with actual Laserdiscs either with so many options today, but some of the nice rips available might be worth a look — especially if you’re nostalgic for the colors and feel of Star Wars from the 80s/early 90s.
Silver Screen Edition is a scan of a different print of SW that predates 4K77 and has essentially been superseded by it I believe.
There’s also always the option of the various Special Editions, of course, but for me that’s unacceptable except maybe for Empire, which was the least butchered and only has one change (“Bring my shuttle”) that really bothers me. The new 4K scans on Disney Plus have great detail and color, so you might consider that for Empire at least if you likewise aren’t too bothered by its changes. Until 4K80 is out I just might put up with it myself. And some people have made “semi-specialized” fan edits that retain only the SE changes they like. You might look into those too if there are things about the SE you prefer.
That about covers it I think.