I'll try to give my opinion on some of the games as starting points, you pick the one that sounds the most applicable to you.
> Ultima 1
Only if you are curious and have a lot of patience. This game was basically a teenager throwing shit at the wall and seeing what sticks. Nonsensical game mechanics (you gain HP by exiting a dungeon after killing monsters), there are very few directions on what to do and once you know what to do it becomes uninteresting.
Ultima 1 is innovative in that it had a completely open world and it was more about figuring the world out than killing monsters and grinding EXP. It's interesting for its historical impact, but not that interesting as a game in its own right.
> Ultima 2
Everything I said about 1 applies to this one as well, except it's even more obtuse. If 1 was not a starting point for you, then 2 certainly isn't. One of its big new innovations was that turns pass even if you press nothing, making it a sort of early action RPG.
> Ultima 3
Now we are getting somewhere. This was the first game published by Origin, so Garriot could not goof around anymore. Much more refined gameplay, different classes and races, a party system, tactical battles, useful dungeons and better directions. It's still very rough, but I consider it playable by modern standards. Just make sure to get the upgrade patch and use the option that cuts down of food consumption.
> Ultima 4
Here is where the actual story of Ultima begins. The first three games are technically canon, but it doesn't really matter. Just watch the Spoony videos if you want to know the story. 4 is where the story of the Avatar begins, the virtues are introduced, the geography of Britannia is established, and where the characters are introduced. Plays pretty well and food consumption is finally sane in this game. Combat can become tedious if your party is too large, so pick only one or two companions until you get ready for the final dungeon. And keep a journal, you will need it.
> Ultima 5
A somewhat more refined version of 4. If you can play 5 you can also play 4, so start there.
> Ultima 6
Get the Nuvie source port:
http://nuvie.sourceforge.net/
https://github.com/nuvie/nuvie
It lets you play the game natively and has an option for a better interface. The new interface is the way to go, and if the previous games are too archaic for you, then this should be just right.
> Ultima 7
A lot of people recommend 7 and consider it the best in the series, but I hate it. Interface is awful, gameplay (especially combat) is awful. It does have an interesting story and interactivity that hasn't been matched to this day though. But let's be honest, you'll only bake bread once or twice before the novelty wears off and you see that Ultima VII is just a point & click adventure with convoluted game mechanics. It's the sort of game you play for the story, or to just derp around in the game world
> Ultima Underworld
This is a spin-off, but it's a great starting point because it has only loose connections to the main series. The interface is surprisingly good, it has no mouse look, but an early form of WASD-controls and all actions can be carried out with the mouse. Make sure you read about "default interaction mode" in the manual, then you won't have to use those weird buttons on the side of the screen and it will play almost like a modern game. Also, an auto-map that you can take notes on, fucking sweet.