Wouldn't consider a levergun?
The guns I own that I would teach with are:
1) Start with the Ithaca 49 "boys rifle". Single shot, hammer cocked by thumb. Unfortunately survivors are no longer cheap.
2) Progress to Marlin 39M (or A). Adds repeater, sighting options and overall quality. A lifetime rifle.
Both shoot any .22 rimfire (non-mag).
Don't own one, but that Ruger American compact (12.5 LOP and just over 5#) looks like good kit in the modern day that can grow with the user. I was intrigued with a Browning T-bolt (straight throw) I was viewing at Cabelas gun room the other day. CZ makes a nice rifle, but IMHO more in tune with adult sizes aside from the Scout model.
I'm also going to differ from learning on "buckhorn" sights with young eyes. Same sight picture they'll use when shooting pistols. Open sights also promote environmental awareness vs. tunnel vision. Most my rifles and some pistols now have optics or lasers, but old eyes largely drove that decision. Success does drive confidence, but fun drives desire. A lever .22 is FUN.
"Accurate" can mean many different things. Minute of soda can or cloverleaf. With reasonable goals for the platform, success is readily achieved.