Also, 7mm-08 would be a good choice but I think the 25-06 kicks even less and would shoot flatter.
Not that faltter and recoil is about the same. I can launch a 140 grain bullet from my 7mm-08 Rem at within a few feet per second as what you can shoot a 120 grain bullet from a 25-06 Rem. Actually I often wonder why there is a 25-06 since the 270 Win will cover all its bases and then some.