Congrats on being reunited!
My husband and I are only just now opening a joint bank account, and I've been here nearly a year and a half. Part of it was the credit situation, but mostly it was just that I already had my name on enough other things that it wasn't necessary. Transferring money to other people is so easy over here that there was no rush.
I'd add her to the utility bills and council tax, as well as getting her registered with your local GP. The GP registration will trigger a piece of mail in her name so that's a good start. When she gets a bank account, make sure she opts to paper statements as that will be very helpful too. As for national insurance, I believe since she is coming in on a visa issued from outside the UK that you just need to call and they will send you an application. I could be wrong on this because the way they do things seems inconsistent. The other option is that you'll call and she will have to attend a simple interview to be issued her NiNo. Either way the whole thing will probably take about 8 weeks. Getting a mobile phone contract can occasionally be tricky due to lack of credit, though I had no problem getting a 1 year sim only contract (I'd bought the iPhone 6 outright the day it released) from 3 about a month after I'd arrived in the country. I just hero provide information for direct debit. She could also go ahead and apply for a provisional license. She'll be able to drive on her American one for a year anyway but it'll be another thing she can do in the first few months to get set up.
All these things should trigger a decent amount of mail in her name so that will be really good for your future FLR application. You could even spread some of the less urgent things out a bit (maybe GP registration and the provisional license) so you'll have stuff to cover the time periods evenly on he FLR app.
Additionally, I'd switch any bills that you currently have as paperless to paper. I know there's sometimes a free for this, but it will save you a lot of stress down the line.
That's all I can think of off the top of my head. It's good you've got a week off to help her settle in and get all this stuff done.
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