Something to keep in mind when reading the above:

BD maybe a great programme, but there is a 99% chance that it will be subsumed into Lh within the next year.

Regarding the Skyteam assertion from Mike above, I really do not understand it, as other than probably Australia where Oneworld does have the edge, I do not see how ST has less worldwide covergage than 1W.

My 2 cents in terms of ease of earning/maintaining and benefits would be TK for Star, OK or DL for ST, and probably AA for 1W. Then again it really depends on flight patterns and class of service. If she's going everyhere on premium fares and mostly long haul she may find BA and LH better for her......