Personally I would start with ultima 4. Play it for a while (since it is free), get a sense of what they are trying to do, and then move on.
The game play doesn't stand up today. The ideas? You may find them very interesting especially if you are more used to the modern take on what an rpg can be.
Jump forward to 6 then. This is probably my all time favourite game. Sure 7 was better in a lot of ways, but the things you can do and the sense of exploration in 6 is pretty much unmatched.
You may or may not love this game, I hope you do. When you consider you can make a mouse carry around a halberd, well how can you go wrong?
7 is generally considered the peak of the series. There are some rough, unfinished parts here and there (the peak is not an exaggeration, you could see the cracks appearing) but graphically it is still great and has some interesting ideas. To me, it was just a little too streamlined after 6 and a move in the wrong direction (something that still happens to this day).
8? Well it hardly seems like an ultima game. The first hour or so is really the best part of the game, with the rest bordering on the generic. I would almost skip this one.
9 got a lot of criticism when it came out and rightly so. However the first moment I sailed into bucaneers den in 3D is still a high moment in gaming for me. I would get it, play around a bit, but don't dig too deep.
In terms of spin offs, I found the two U6 "expansions" really quite interesting to play. If you get into 6, give these a good go as well. It's a shame that these worlds were not more fully explored in later titles, as there were some interesting gameplay mechanics, especially related to the dinosaurs.
I never really enjoyed ultima underworld as much, but they also get a lot of love. 2 was certainly a lot better than 1, so give that a good go too.
Enjoy! I have been waiting for ultima X all these years. Most likely i don't want it anymore, considering what it would become. But you can still have weeks to months of fun in some of the most beautiful and interesting worlds every produced.