It depends on where you fly the most. My preference is Star Alliance because BA miles cannot be earned on AAdvantage for trans-atlantic routes. Even if I could earn it, BA only gives 30% for discounted economy class. On the other hand, LH and BMI miles can be earned by UA Mileage Plus. Also, for trans-pacific routes, CX miles can be earned on AAdvantage only if you buy H class and above. AA does not have any flights beyond NRT without relying on code-sharing flights, but UA has. AA code-sharing with JL often is over-priced.

Among BA, LH and TG, my preference probably is LH unless TG is using newer aircraft for that route. TG's B747 is so old and it is almost scary flying with that aircraft.

Hope it helps.