I started my #2 son on a 260 @8 years old and 100 gn loads now I've upped him to heavier 120 gn loads and I have 500 Nosler 140 gn Part in the wings for this gun and another 260 later. I chose the Rem Mod 7 and he really loves it and shoots it well. He took his first 2 animals in SA with it, and the 100 gn Nos BT went right through both the steinbuck and surprisingly the warthog as well.
I wouldn't knock the 7-08 either though in a Mod 7, my whole shooting family loves the Mod 7 as a short, handy, quick pointing and light little gun. Bought #1 son a nice little CDL Mod 7 in 243 for his Bday a while back and it is his most used rifle now, #2 son has added my 358 Win Mod 7 (courtesy of Why Not?) to HIS collection and shoots it most frequently, while I still have a Mod 7 MS in 7-08 and another Mod 7 in 350 RM in an old KS version with the fiberglass stock.
I highly recommend this rifle and any of the chamberings it comes in, especially if you hand load. It also comes in a youth model and you can buy replacement stocks for them for 99 bucks later on to fit as he grows. I did this with #2 son's, I bought him a CDL and then a plastic stock at WSS for hunting, while keeping the nice CDL stock, nice. These rifles fit very well and all of ours shoot 1 1/2 moa or better, in all the above mentioned calibers.
The 260 will also do a very nice job as a varmint rifle with the light bullets which you can zing along quite respectably and then head for moose, elk, deer, caribou, sheep or what-have-you with 140 gn Nos Parts or 130 gn Nos AB which is my new favorite hunting bullet.
Just my experience for what it's worth.
#1 son bought his girlfriend a Win Mod 70 Ftrwt carbine in 308 and she loves that rifle and shot 3 bears last spring with it, including her first grizzly. She is very petite and the gun fits her perfectly and shoots 150 gn bullets (mine, of course) into sub MOA, loaded around 2600 fps. I would say this rifle in 7-08 might also be a winner, especially if you are a CRF freak, and feel it necessary to chamber a round while upside down, spiraling out of control, free falling from an aircraft at 120 mph, while skydiving!!! Myself I'm totally bifeedual and don't really care one way or the other.