Free: Contests & Raffles.
When my boy was 8 and he started I bought him a little Savage youth model 11 in 7mm-08(came with a little Nikon 3x9) and its been a sweet little rifle for him and he's 12 now. He's take a couple deer out passed 300 with it. I load 120 gr Barnes TTSX and it's done the job on both elk and deer for him. The scopes not the best but plenty for a youngster I think. I think I paid $475 for it new.
Ruger American Compact 7mm08. You can get factory 120gr loads that will kill any deer and only about 3# more kick than a 95gr 243. Best part is she can move up to a 140 or 150gr bullet with almost the same exact ballistics as the ever so popular 6.5 creedmoor. No 243 can do that.
I think I'm going to go with the 308 Winchester for my daughters (9 & 11 years old.)I can download it to begin with, using 125-130 grain bullets at around 2,300 feet per second. That will work just fine for deer out to about 200 yards.If they end up hunting elk, bump up to a premium 150 grain bullet at around 2,800 fps and it's now an elk rifle.