Welcome to the UK

If your experience base is mainly US legacy carriers, you might find these UK-centric ideas helpful

1 BA is a much better bet than you might expect if you get a BA Amex card which (on the right version) gives you a 2-4-1 voucher for a BA miles trip for only spending £8,000(?) on the card. Plus you can earn a stack of BA miles by shopping at Tesco (leading UK supermarket). And if you use Marriotts enough, the Travel Packages let you transfer from Marriott Rewards to BA Miles on pretty good terms. The bottom line for us is that we get 2 x BA First Class long haul each year while hardly ever flying paid BA. Longer term (but who knows really) BA and AA seem likley to integrate/merge their frequent flyer schemes more closely so the case for maintaining AA seems less.

2 There is such a strong network of LCC carriers serving almost everywhere in Europe at such stunningly low prices that I almost never fly legacy carriers in Europe these days. The cost savings are just to great to ignore. Plus LHR is such a congested airport that time savings along make Stansted, Luton etc worth considering, although this depends slighly where you live/work. And you can get paid lounge access is its really valuable

3 On the Star Alliance front, BMI's scheme is pretty interesting as it permits one way awards plus cash + points awards. I think its also possible to take a LCC trip to Europe and then pick up a free long haul premium class trip (on LH, for example) for lower mileage rates. Mind you, most people seem to assume BMI won't be independent for much longer, with LH seen as an obvious partner.

***
Finally, the various stickies on each of BA, BMI etc are very helpful

Good luck and good flying