The very first cartridge that comes to mind is the .25-06. The second cartridge that comes to mind is the .243.
Granted, both cartridges can effectively kill both deer and varmints (given reasonable shooting distances, bullet construction, and, most importantly, bullet placement.)
I think that it boils down to this - if you are going to be shooting more deer than varmints, then get the .25-06.
On the other hand, if you will be shooting more varmints than deer, then get the .243.
Zachary