My first piece of advice would be to shoot a 7x57. Soft on the shoulder and tough on game. Big punch in a little case.......... wonder who said that????
I don't have the experience that all y'all have, but in my particular hunting environment, that is my experience as well. I don't need something particularly heavy - even the .30-06 would be "heavy" where I hunt - and speed and distance really isn't an issue either, unless I'm shooting along a right-of-way. For me, the 7x57 simply fits the bill: gentle on the shoulder, I can stay in the scope after the shot, does exactly what I want it to do. There are probably a dozen rounds that can do the same thing, exponentially more if handloaded. I just like the old Rigby load.
