I'd go for Ultima Underworld first, just because you are on your own, you only have to manage one character and the world is more condensed. One thing I have noticed is that Britannia kept getting larger and larger with every game, this might have been great for long time players who were introduced to the land with Ultima IV and had an idea where things were in relation to each other, but the later the game, the harder it is to get into instead of just drowning in content. In Underworld the world was new to everyone, so you don't need to have background knowledge about the world.
I first tried playing the games in the order in which they were released, but after the first trilogy (which you can skip, it's only for those who are curious) I went to underworld instead of of Ultima IV. Now I'm playing Ultima IV and while the game was quite fun at first it has become a tedious drag, by the end you need to have a full party and every combat encounter drags on forever. Using walkthroughs on the internet I was able to figure out the most efficient paths through the dungeons and quickly get it over with, but in the final dungeon tricks don't work anymore.
Also are the Underworld games part of the storyline of the normal Ultima games? I read somewhere that they aren't considered 'canon'?
They are kind of squeezed into the overarching storyline, so you won't miss anything if you didn't play the main series and you won't miss anything if you skip Underworld. The only thing you need to know about is the whole "Avatar" deal with the virtues and stuff, but you can just watch Spoony's retrospective to get the idea: http://spoonyexperiment.com/category/game-reviews/ultima-retrospective
Just keep in mind that Spoony is an entertainer, not an actual critic, so take everything with a grain of salt (all the complaints about Underworld II for example are not valied at all). The series really got started with Ultima IV, the first three games are more like experiments.