Generally speaking, I would choose the 280 or 6.5 over the 270. Reason: BC
The 280 is a great cartridge (I have one: My 280 - Updated!
) and you can shoot 168 and 180grain bullets at good velocities with a barrel as short at 24".
The 6.5-06 is another great choice as you can get the 130 and 140 grain bullets going screaming fast (3100+).
I would lean towards the 280 as no fire forming of brass would be required. that's just my preference though.