I would go for a 308 as it will do all you want and more, plus ammo is avliability is not a problem.

If you can get an AR style rifle in 308 in left hand I would seriously look at this. Most can match bolt actions for accuracy so your long distance and close scrub shooting is taken care of. I do not advocate semi autos for the reason of puting a ton of lead in the air but for a quick follow up shot. With a bolt action your master hand has to break its grip to work the bolt and then come back onto the rifle. With a semi auto both hands stay on the rifle and you reaquire your sight picture faster. the time difference is small.

Some AR type rifles carry a fair bit of weight so you would need to check this out and you want a hunting base rifle not one with all the military gear attached.

Scope. I have been told by many with far more experience than myself that it pays to spend more on your scope than your rifle. While my experience backs that up, with the quality of todays midrange scopes-Leopould, Nikon, Zeiss Conquest etc, I do not think it is so important now.

The above is just my opinion and maybe worth thinking about.