Ultima 1 and 2 were archaic 20 years ago when I first tried to play them. I’d say don’t bother unless you want to say you played them all. Ultima 2 in particular is really oldish, since Ultima 1 at least got a makeover in the mid 80’s when they ported it to the PC.
Ultima 3’s a bit better, but still really old school, and doesn’t really offer much to make it worth putting up with the outdated graphics and clunky mechanics. Maybe if you really wanted to play it check out the NES version so at least it doesn’t look quite so bad.
Ultima 4, looks really old, but really took things in a new direction from “kill and/or loot anything that moves”. If you can deal with keyboard based controls and the graphics, definitely worth playing at least once.
Ultima 5 took everything Ultima 4 did and refined it and set it on top of a really dark story about zero tolerance and extremism. Again, well worth playing if you can deal with the interface.
Ultima 6 may not look great today, but for it’s time those were some awesome graphics. They added mouse support, but it’s not really well implemented yet, and may take some getting used to (keyboard support is still there, too). Worth playing, definitely, as are the two spinoffs using the same engine, Savage Empire and Martian Dreams. Martian Dreams in particular I would recommend for all the cool Victorian stuff and cameos from real people in that era.
Ultima 7, anyone who has even the slightest interest in Ultima needs to play this. Mouse is now actually intuitively implemented, graphics look top notch for 2D VGA, and it’s just all around awesome. MOST HIGHLY RECOMMENDED
Ultima 8, kind of a step back from 7, but if you’re still itching for more after 7 (and 7 part 2) this isn’t too bad, just don’t set your hopes too high.
Ultima 9, meh. Fairly generic 3D RPG with some Ultima stuff floating around in it. Very disappointing as an Ultima, but not a totally horrible game to avoid at all costs either.
There are also the two Ultima Underworld games, some of the first games to really do a 3D world, which is astonishing since it came out before Wolfenstein 3D (which gets a lot of the cred) but it pushes things a lot further than Wolf3D or even Doom. Not sure how they’d hold up today, but really groundbreaking stuff.
But which to start with. Well, if you can stand the graphics and keyboard, Ultima 4, since that really sets the stage for everything after it (and via some retcons even some of the stuff before it). Otherwise Ultima 7.