RE: .243 or 7mm-08?
Given a choice between the two you noted, I'd go with the 7mm-08. I've used a .243
years ago for deer hunting, and found it a bit on the light side (mule deer). Ok for antelope though.
Any case, for the uses you noted why not take a look at the .260Rem. A friend of mine has one, and uses it on whitetail with no complaints at all. Take a look at the Remington
700 LSS Mtn. rifle (stainless with lam. stock).