Some years ago I wanted to do the same thing. I first used a .308 Win. I did not feel much reduction in the recoil.
So that rifle became a .257 Roberts. It has very little.
I also have a .25-06 and it has very little recoil.
So I would say use either a .257 Roberts or a .25-06.
But there is nothing wrong with a 6.5x55 Swede or a .260 Rem.
There are no bad choses here, pick one.