A light centerfire for my son so we can deer hunt together. He'll start on the .22 in the next year or two.
Guess I should have taken a moment to read your post. I took the title as an "at large" question. Please accept my apology for being so rude. Of those 3, the only one I own is a 10/22. It is a hoot and fun to get new shooters hooked on. However, if the .22 you have is a good one, then your next rifle should probably be one of the other choices. I have a model 700 Mountain Rifle in .30-06 and it is a great all around hunting rifle, so the .308 would be as well. If you are mainly going to hit the range for fun, the AR is a pretty attractive choice and the one I would choose.
In most forested areas, 100 yards is plenty good. Several good hunters I know sight for 200 yards so they can pretty much hold dead on for any shot up to 250 if they have a flat shooting caliber. We have heavily wooded areas here, but sometimes a long shot is available across a farm field.