I don't know where you will be hunting in Fla., but unless you're on a cattle pasture, its hard to see a deer at more than 200 in the palmetto's. As for the Ar-10, you'll have to make sure you've got a 5rd magazine for it....here in Fla. you're not allowed to have more than a 5 shot capacity in semi-autos.
30-06, 308, 300mag.....bigger or smaller.....I've used a bunch of them here, and they'll all do what you need. Just make sure you save enough for a GOOD scope.....foggy mornings and hazey evenings play havoc on glare.