I second the 257 Rob. suggestion.
Great cartridge.
How about the 260 Rem?
I've shot several 7mm-08's, great round but borderline recoil for smaller hunters. Started my wife out with one for deer and changed to a 25-06, she is much happier at the bench. She's left handed, that's why she didn't get a 257 Roberts.
The 243 is the minimum for me, I've harvested plenty of deer with this cartridge, good 100 grainers will kill deer just fine.
I started my boys, now 10 and 12, with pellet guns, 22's, then 20ga.
Now the both shoot my 257 built on a mauser action. The oldest gets to hunt this coming fall and will carry the 257. My youngest gets to go next year, so he will get the 257 and the oldest moves on to my 6.5x55 Swede.
Before they are 16 they will have their own 30-06, a 22 rifle and 12ga.