I wouldn't be too worried about a frequent flyer program in the short term and just shop on fare. I primarily use Google flight explorer and I know many also use ITA Matrix. They give you some flexibility in searching multiple airports or airports within a certain distance of your origin/destination.
https://www.google.com/flights/
https://matrix.itasoftware.com/

With UA and DL, an $800 ticket is only going to bring in around 3,500 miles, so not much when a free domestic ticket is 25,000 miles. At AA, you'll do slightly better with around 9,000 miles RT via JFK, but again not too much you can do with 9,000 miles. If you start flying for business these numbers can change significantly with higher priced fares (DL, UA), but I'd wait until that day comes to pick a carrier or alliance.

One thing that could hurt you is flying around Christmas. Fares tend to run higher at that time of year versus early December or later in January.

Your bigger expense could be accommodations, particularly if you're planning on hotels in London. Are you going to do hostels or stay with friends? I wouldn't buy an airline ticket until you have a good handle on ground costs which could include not just hotels but rail or flights within Europe.