I will buy either a 260 Remington or a 7mm-08 for each of my kids as they get old enough to hunt. They can easily be loaded to the same recoil level as a 243 Winchester, but they are far more flexible. With bullet weights going up to 160 grains for the 260, or 175 grains for the 7mm, loads can be found that will work for any non-dangerous game. This allows the rifle to grow with the hunter. In the same vein, the 6.5x55mm, or the 7mm Mauser would be good choices.
Of course, since this is the T/C forum, we're really talking about first barrels, I suppose. One could always start with a 243 barrel for deer, then track down a more flexible cartridge later.