In case Peter doesn't answer, my personal experience has been that you'll want a more stable work visa than an H1. Given your skills, one of you should be able to get one (and the other can come as a spouse and apply for a work permit with the right visa type). After a few years with that, you can apply for a green card (permanent resident status). I know people who have renewed those for decades without becoming citizens. Or, after a few years with the green card, you can apply for citizenship.
I know lots of Brits and Canadians in California who have also followed this path.
A lot of talk in here about H1B visas, and that's probably because they're the most plentiful. But, that's not the only type of visa that people should be thinking about.