For a given Outside Diameter, like the Encore where barrels are profiled the same on the outside (there are exceptions),
the bigger bore diameter makes a lighter rifle because there is a large hole (ie, less steel) while the outside stays the same. However, lighter weight + larger bore = increased recoil. So there is a tradeoff in weight vs. recoil.
I see no reason to choose a 7.5x55 over a 308, as I have both and they kick about the same.
A prohunter buttstock will do wonders if you don't already have one. After that, as suggested, the 7-30 Waters, 257 Roberts, 243 Win are all good choices. So is the 7x57 Mauser and 6.5x55. However, the easiest one to find ammo for is the 243.
JW