IMO, a .22-250 would be good, just make sure you keep the shots within 200 yards for deer, and don't attempt a shoulder shot. The best shots for a .22-250 would be either vitals, or neck. When it comes to neck shots, make sure you don't shoot more than 100 yards.

I would not recommend head shots with the .22-250, you need a bigger cartridge for that.

There are all these people on this site that are going to brand you as unethical, and claim that there is no other shot than a broadside, right behind the shoulder.

That's crap, the key is, don't push yourself beyond your shooting ability, if you can hit deer in thehead from 300 yards away because you're that good, good for you, if not, don't try it.

So like I said, the .22-250 would be the best since you want to do lots of varmit hunting too.