If you are looking for low meat damage and low recoil, choose something like the 243, 6.5x55, 260, 257 Roberts, or even the 7mm08. I am a 257 fan myself, but all of them are good choices. The bullet selection is just as important, so pick something that won't explode on impact but keep intact and mushroom nicely. I have seen a 243 tear a deer shoulder to pieces, but a proper bullet makes one nice clean channel.
My cousin cuts up over 300 deer a year for folks, and the most damage are usually from the light bullet/high velocity types like the magnums and short magnums. The heavy bullet magnums do very little damage, and I use a 375 H&H quite a bit on does since you can eat up to the hole with less damage that most calibers. The recoil would be too much for your criteria though.