My 11 and 14 year old learned about lever actions in their hunter safety training.
Are Marlin 336s worth a dang anymore with Remington going belly up?
Should I get a Henry?
First, I would strongly suggest a
Henry Small Game Rifle with the peep sights! 22LR is a great start but, personally, I'm on the hunt for a 22WMR version.
The Marlin 39A (own one) is nice but, at over $1,000 is just to spendy these days. The same can be said of the Winchester rimfire but, I don't own one myself though my friend uses the 22WMR version for varmints on his property.
If you want a centerfire option, one of the Italian 45Colts or 44Mags would be my first choice. The newer Winchester 1892's are sweet but, easily over $1,000 too.
The old Marlin 336 30-30 my father had and I just didn't bond well. It is a fine rifle but, we just didn't meld together well. Today, I would probably try a Winchester 94 angle eject option in a 35/375 version.
That being said, a lever-action Henry rimfire is an awesome choice IMHO. YMMV