I say go with 1/2". Have them use screws, not nails, and make sure they don't skimp on the screwing. The sheets should run perpendicular to the joists AND should be installed BEFORE the walls are 'hung'. Make sure the seams are taped and mudded even if you're popcorning the ceiling. Make sure they do at least 2 coats on the joints, 3 is best.
Other than that, that's my $.02 ... My best to ya and hope this helps.