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).
I'm also going to differ from learning on "buckhorn" sights with young eyes. Same sight picture they'll use when shooting pistols. 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. With reasonable goals for the platform, success is readily achieved.
"Accurate" can mean many different things. Minute of soda can or cloverleaf.