I just picked up a cz 527 in 7.62x39 for the same purpose as you. The rifle is a slightly more expensive than what you're looking for but the ammo is cheaper so you save in the long run.
Low recoil and the rifle is fairly light.

Savage has recently introduced the AccuFit stock. It has adjustable LOP and adjustable riser heights, so your daughter can shoot it when she grows up, maybe, although my wife likes her youth model Savage in .243. I am searching the internet and Gunbroker for a Savage 110 in 6.5 Creedmore. It is available for around $525 on the internet, with a Vortex Crossfire II scope included. Savage makes these in a variety of calibers.

Well, after doing some more research and handling a few rifles...

We decided to go with the Marlin XS7 in .243

For the sale price CDNN had them, it was a great deal for the rifle package to get her started. This had really great reviews. I know they are not making them anymore but for the price and quality figured we couldnt go wrong.

We like that this had more of a classic feel/stock compared the the Ruger / 783 rifles. Bolt and trigger feel great. Didnt break the bank so if she doesnt get into it, no worries at all. Will be a fun range rifle or maybe I'll even give it a go out hunting. Its a bit lighter than my Savage.

If she gets the bug, I'll look into upgrading her and use this one as a fun plinker. My significant other loves to shoot at the range, but has no desire at all to go hunting. Would get passed over to her probably. Either way, it will fit into the rotation



Now to get to the range. Need to set the scope distance up for her still as well.