What order should I watch the Digimon Adventure series?

You've basically hit the nail on the head with the original list--you've listed almost all related tv series/movies in the Adventure canon in about the order that they came out and are chronological in-universe. There is a movie, Revenge of Diaboromon, that takes place after Digimon Adventure 02, that you missed, but I myself had forgotten about it. You would be able to keep up fine and miss out on nothing by watching it in your order.

Now, Digimon: the Movie is the English release of three different animated features smashed up into one 90-minute movie: Digimon Adventure is technically a prequel to the first season (and, in Japan, was released prior to the series), Our War Game takes place after the first season, and (deep breath) Digimon Hurricane Landing!!/Transcendent Evolution!! The Golden Digimentals takes place midway through 02. So, if you insist on watching the English movie, you'd probably want to watch it before episode 20 or so of 02. As far as I know, the individual features have never gotten an English release, though you could certainly find fansubbed versions if you looked.

The other seasons are completely unrelated to the Adventure canon, although most are worth watching anyway, if you have the time and inclination. As you said, the climax of Fusion/Xros Wars involves all of the previous seasons' characters, including the Adventure kids, popping in to cameo, but this doesn't affect the Adventure plotline in any way. I think you'd be hard-pressed to find anyone who considers their appearances part of the Adventure canon.

Digimon Universe: App Monsters is another self-contained universe. Digimon Adventure 2020 is a hard reboot of the Digimon Adventure plotline.