i bought my son a Savage 25-06 Axis II XP last year. at under $500 it seemed like a good starter package with the Bushnell scope. the same rifle is available in .243 and 7mm-08, so i considered those as well.
i chose the 25-06 based on the spectacular ballistics: very flat-shooting out to 200yds and with great knock-down energy. it’s essentially a 30-06 cartridge narrowed to shoot a .257/6.5mm round. there’s a wide range of factory load options (though currently hit-and-miss like everything) including being able to push a slightly larger grain bullet than what a .243 likes to do. one drawback for youth is that it does need a standard size barrel, so no short “youth” model, but my kid’s already over 5′ tall so he can shoulder it effectively and handle the 7lbs just fine. i’ve been very impressed with it’s accuracy and grouping out to 100yds on the range. recoil is quite modest shooting a 117gr bullet.
my son’s 9, so in MN this year he carried it unloaded to practice carry safety and scoping in real life on some does. to this point he’s only fired it in a lead sled, so over the next year we will need to work on firing from his shoulder on a rest to get used to the recoil in preparation for hunting next fall. he could hunt this year back here in WI, but he needs more work with the gun first and another year will have him more mentally ready too.