I noticed after posting that you asked about models. After checking around, I ended up buying an N.E.F. Pardner in 20 gauge. The Pardner is built solid, yet doesn't weigh too much. It's a single shot (no worries about the kid turning around to celebrate a hit and blowing your butt off with the second shot). 20 ga. ammo is easy to find, affordable, and a good load for beginners.
Best of all, the gun costs less than $200.00, GST included and comes with a lifetime warranty.
SIDE NOTE: Even though the Pardner is way too small for me, I've taken it into the field. The fit sucks, but it was so light, it was a pleasure to carry all day. Didn't miss any shots because of the fit, so I didn't regret shooting with it.
SS
edited to add comment about 20 ga. ammo