Firstly, those are all medium bores, big bores start at .375 H&H, but it doesn't sound like you really need a big bore.
For an accurate rilfe you could do a lot worse than a Savage with a good aftermarket stock, and .308 is a good round for that.
Of the hunting calibers you mentioned personally I would be comfortable with any of them. I regularly hunt with a 7mm Mauser (similar to the 7mm-08), and .270, .308, 30-06, .300 Win Mag and a .458 Win Mag. Of those you mention I owuld probably pick the 7mm-08, with light 139 gr. loads it's suitable for all deer size game, and with 154-173 gr. loads I'd be quite happy with it for up to Elk size. And the big bonus is it doesn't beat you up. The 7 mag is just more of the same, and in most instances the extra recoil isn't really needed.