There are what I'd call strictly shorter range calibers like the 30-30, and there are good "lighter" calibers like the .243 or .257, that are not neccesarily "short range" calibers!
So, my question is what is it you are looking for? If its really lighter recoil, I'd go with anything from the .243 on up to the 7MM-08!
Unless I'm bow or handgun hunting, I don't like to limit my range, even if 95% of the shots will be short, 'cause there ain't no such thing as a "brush buster!"
As I've said before,"you can make a short shot with a long range caliber, but you can't make a long shot with a short range caliber!"