My personal favorites are 6, 7 (complete) and 8. I know that people have their reasoning for liking the older ones, and I do understand that the worlds are bigger in those, and for anyone that played them when they came out, nothing else could recreate that experience.
However, 6, 7, and 8 had amazing soundtracks, beautiful visuals (even today the art style is very interesting) a lot of depth and more fleshed out stories, and their atmosphere (the sum of all these parts) just pulls one in. (In my case anyway) I actually had seen and played the earlier ones a bit, but they never really got my full attention way back then. The one that finally really pulled me in was Pagan. The music alone set a dark and atmospheric tone, the down-trodden citizens eerie locations, interesting magic (if a bit awkward to cast in some cases) etc. were really a good introduction to Ulima for someone that hadn't played any. Each weapon in the game has an in-depth back story, there is plenty of history to the world of Pagan, lot's of books, etc. I hadn't played something so in depth (well, aside from System Shock which I played sometime around then.)
I played 7 afterwards, and it was my real introduction to Britania, and the more classic setting of Ultima. 7 also has a wonderful soundtrack, the party system, a lot of really fun secrets to discover, etc. This was my inspiration for playing more, which ended up being 6. 6 is like a mix between the modern and classic interfaces, and while a bit more primitive, had the same impact on me as 7.
Also, while it's no 6, 7, 8, and while it has many many shortcomings, if you patch it up, add the community patches, replace the speech with text (another patch) and can tolerate a some major differences, Ascension is actually a pretty good game all on its own. Is it a good finish to the series? No, absolutely not. Is it a good Ultima game? Yes and No. It has nowhere near the scale of the earlier games, but it does have a half-decent story, if a bit truncated, great soundtrack again, some very interesting locations, secrets, and some unfinished locations that actually add IMO to the mystery of the game. IMO the game's scale is so much smaller because it was pretty early in the game for expansive RPGs with 3D graphics. I think the switch from 2D to 3D at that time really limited what was possible for a game with the scope of Ultima. (not to mention the artificially set much-to-early release date that the monsters at EA imposed on the devs)
Anyway, I don't think you can really go wrong with an Ultima game, even if you basically play them backwards from the inside out :D like me. As far as feeling at home after playing UO though? Probably 6/7/8.
I have yet to play the Underworlds, but since they're like a mix of System Shock and Ultima, they are definitely on my list of must play games.
Anyway...