308 based cartridges work well in short barrels, so I would recommend anything in this case. The 260 rem, 7/08 rem, the 308 win and the 6.5 cm all work well.
The 7/08 would be my first choice because of velocity and bullet choices. (I have all three cartridges) I don't recommend heavy bullets because of low velocity that effects bullet performance in many bullets.
My 7/08 can push 140 grain bullets to 3000+ ft/sec in a 20" barrel without excessive pressure, and 120 s to 3150+ft/sec.
Any of the fore will do a great job in a short barrel so you have choices.
J E CUSTOM