Depends on whether money or power are considerations or not.
If money is a consideration then picking one of the small or medium bores that are common in Europe like 7x57r, 7x65r, 8x57r, or 9.3x74r opens up a large number of relative inexpensive European double rifles. If power is a consideration, 9.3x74r, 45-70 etc. are excellent choices.
I've used 9.3x74r and also 7x65r on a fair number of game. I'd say the 7x65r would handle most anything in the lower 48 USA. The 9.3 makes a lot of sense if you are hunting heavier game like elk, bears, moose, etc. If its mostly whitetails and hogs the 7x65r will work well.