I've probably owned more handguns over the years then I have rifles but out of the ones that I have owned the ones that come to mind were a Ruger M-77 in 220 Swift, and a Savage 99 in 300 Savage ctg. I think if you can find a Savage 99 in 308 Win or even 243 Win it'd be an awesome woods gun that'd still give you quite a bit of range.
Of course after doing a bit of research and reading my next high power rifle will be in 25-06 Remington. Not sure which one yet but that's the cartridge that I want to go with because it has low recoil, can be used for large varmints with lighter bullets and deer(and even elk) with heavier bullets and it's just "odd" enough for me to like it but still "standard" enough to find ammo and reloading stuff for it.