My daughter and niece both started out on Weatherby Vanguards in 243...when my brother and I bought the guns they came with both adult and youth stocks (not sure they do now days)...the rifle certainly isn't the cheapest out there, but we got a smoking deal when we bought the 2 we have....accurate as heck out of the box and the Howa 1500 action that they are built on is outstanding. That being said, my daughter moved over to a Savage 11 I built for her this last year in 250 Savage.
There are some decent cheap rifles out there like the Ruger American, Savage Axis, Remington 783, Mossberg, H&R Handi Rifle...of these the only one I actually own or have any experience with is the H&R...I have one in 243 and it's a real good shooter, but I am not sure I'd buy one for a first gun...break action rifles just don't seem to be great rifles to teach on.
If it were me, I'd spend the little extra and buy a Weatherby Vanguard (youth), Savage (10, 11 or 12), Remington 700 or 7...stocks will be easy to find if you need to shorten or lengthen them and the quality is just enough more that they will be a rifle for a lifetime.