Good luck with your move and welcome to FlyerTalk.

Definitely don't buy miles. Maybe, just maybe, consider doing a retroactive Miles Booster during the current promo, but I would probably pass on that as well. (you could get roughly 10k miles for 80GBP)

You're still quite far away from a redemption SFO-LHR return. 42.5k miles in economy, 100k in business. (the economy being poor value since you can find cash fares for not much more than the taxes & fuel surcharge on the reward ticket) Buying 37.5k miles (plus taxes and fuel surcharges) is going to cost you a whole lot more than a cash ticket...

If you find Flyertalk a bit intimidating for finding information, there are lots of bloggers (myself included, but I won't overly promote myself...) who have guides for people starting out in the miles and points hobby.

Luckily for you, once you have a US credit history you can apply for credit cards that have big sign up bonuses. That will be the best way to get you on your way to free flights...