If you absolutely are stuck on a one rifle thing then the 30/06, .280, or 7mm rem mag are hard to beat. There are of course quite a few others that would fit the one rifle idea, but those are some good standards to go with.
However, I think you'd be best served with 2 rifles. And if they slightly overlap in the scope of their abilities so much the better.
Instead of going on a wide range from a much smaller rifle for the small stuff and the much bigger one for the large stuff, consider getting a medium caliber for the lower/medium end and another rifle for the medium/larger end. Maybe a 6.5 X 55 in a modern rifle and chamber and a .338 Win Mag for the upper end.
With a pair like this you could always compliment your gun safe later with something on the smaller and bigger end for the future. Maybe a 22-250 and a .375 H&H.
You have been given much advice but ultimately you'll need to get out and shoulder and shoot some examples to make sure you are going in a direction you like.