Mcoy - Take, as an admiral he'll be grateful and help you up the ziggurat of command
Bashir - Take as hes a genetically augmented genius, useful if you land on a unihabited planet
Phlox - Take as last thing starfleet needs is to be accused of only saving humans
..and that leaves Crusher - Not that I have anything against her per se, but her son however...
Yeah, its petty but I'd close the airlock on Beverly - besides, Q or Picard would rescue her, no doubt via some crazy sci-fi magical hi jinx
Phlox stays. If we are doing this based on medical knowledge that they know in the show, well, he's 200 years behind, and the rest of the doctors would have trained on books he wrote, so they'll know everything he knows about all the weird crap he does.
Practically, everyone else is human, and he's an alien. It's the logistics are harder with him, plain facts.