The goal is to get as many miles as possible on as few programs as possible, while still being able to choose which airline to fly based on price.
The AS frequent flyer mile program and the United (*star) or AA (O/W).
Both AA and UA will offer th rougly the same fares and rougly the same routings/choices on their networks and alliance partners. UA might be a better choice since you can earn AS miles on AA and BA and LA but this is more of a personal choice.
By keeping it down to two programs, you maximize the number of miles earned and still have a fairly wide choice of routes and fares.
The only airline that is not fully represented here would be Delta and the sky team alliance--no big loss.