There are a couple of references to earlier games, but if you read the manual then you know enough to just get started with QotA (Ultima 4: Quest of the Avatar). QotA, WoD (Ultima 5: Warriors of Destiny), and TFP (Ultima 6: The False Prophet) kind of make a trilogy (the so-called 'Age of Enlightenment' trilogy) and you can port your character over between one game and the next, but they're perfectly playable by themselves. While TFP has the best story of the 3, I consider QotA my favourite because I love the concept of an RPG without a big evil villain. It's a story of a normal person cleaning up their act and becoming an exemplar of virtue and I love it.

Ultima VII is again perfectly playable by itself, but, yet again, it's best if you thoroughly read the manual for all the background information you need. There's an old joke of Bethesda introducing a new feature for one of the Elder Scrolls games (NPCs have schedules and go about their daily life! You can bake bread!) and the response being that Ultima VII already did that back in 1992.