HiPhish: I'd still recommend Ultima IV as a start. The first Trilogy is basically just experimenting, unless you're just curious about the history there is really not much to be seen, but Ultima IV is worth playing.

Ultima IV is a good start for several reasons. For one, this is where the series got properly defined, it introduced the virtues, the Avatar, it defined the landscape (Ultima I - III all had different landscapes) and it introduced characters who would stay until the end of the series. Prior to that every Ultima hit the reset switch, but this time the games would all build on top of each other. Another reason is that Ultima IV is still relatively simple, whith each game Origin added more to the table and it could be just overwhelming for a newcomer.

Of course Ultima IV has aged very poorly with its hotkey based interface. It's actually very simple once you know how it works, it's just very unusual for today's standards and there is very little feedback. That's why a good person has written a beginner's guide:
http://www.gamefaqs.com/pc/562660-ultima-iv-quest-of-the-avatar/faqs/45830
You can also find useful links in the resource collection thread. I'd recommend the upgrade patch as well, having nice music to go along with the game is very good. I just beat the game a week or so ago, it was really a unique experience, but it takes preperation rather than just jumping in.

And that applies pretty much for the whole series, if you just want to jump in, kill some bad guys or talk to someone with a notification above their had, then you are playing the games wrong. Ultima focuses more on role-playing than just hack&slash gameplay, which is cool on one hand, but on the other it's unusual compared to most RPGs where you get a sword put in your hand and then start whacking suff with it. If you go in like that you will instantly become lost in all that content.

Ultima Underworld is also a very good place to start. You get introduced to the world of Ultima, but the environment and the 3D controls were new new for people back then, so the designers didn't go crazy with the world, you'll never find yourself wondering "what am i supposed to do?".

All that said however, it doesn't really matter where you start if the story is a concern for you. Spoony's review series will fill you in on the basic plots, as do the manuals for the games. Technically you could just watch Spoony's reviews to get what the series is about, but that would be like reading a Wikipedia article about a book instead of the actual book. Plus, Spoony is not a critic, he's a comedian, so his reviews are not really accurate.

PetrusOctavianus: I've played lots of old DOS CRPGs the past couple of years, and the only ones I found virtually unplayable due their clunky interfaces, small view area and poor combat was U6 and U7. I found the more primitive U4 and U5 both more playable. For U6 I instead played the Ultima 6 Project remake made with Dungeon Siege, which was brilliant.

HiPhish: I mean, what good is having the option to play as certain characters when the game mechanics punish you for doing that?