With a 1 in 14, you will probably need to stay light or they won't spin fast enough to stabilize. Try the heavier ones out, but if they punch rectangles in your targets instead of spheres, they are tumbling because they aren't spinning fast enough.
I've killed deer with 50 and 55 grain Nosler BT's out of the .223 and .22-250, but I stick with neck/head shots. I think that little Barnes tsx will be your best bet - excellent penetration, won't fragment, and should stabilize nicely.
