I went through this exact exercise about 10 years ago. At the time I was debating 243, 260, 308, and 7/08. I am glad for the choice I made. Today I would also throw in the 6.5 Cr.
One trick I used that I have finally told my two oldest kids is that I downloaded their practice ammo.
Practice load:
100gr Sierra HP
27 gr of H4895 (60% of max) reduced load of H4895 .60X45=27gr This follows Hodgdon's guideline for reduced loads of 4895
Then work up a good load for hunting season, and don't tell them. I get 3150 fps with a 120gr TTSX.
They will enjoy shooting a really low recoil load that will build confidence. They will hunt with a very adequate elk cartridge.
Both of my older kids love their 7/08 and have killed elk with it.