Hello, Bruce. The little Stevens .22's are nice little rifles. There are others in addition to the Favorite and the Model 44, its slightly bigger brother. The Crackshot is one I like too, although many don't think it's a safe shooter. Safe with standard velocity, IMO.
There are various models of the Favorite, and you might want to know more, especially if you're seeing one for $500!!! Be aware that the .22's get slightly higher prices than, say, the .25 rf and .32rf. Can't easily buy anything but collectable ammo for those two. Expensive.
Here's the best short course on the Favorite that I've found. You might want to read a bit before plunking down your allowance.
http://www.wisnersinc.com/additional_inf...rifles.htm
Some were pretty fancied up (rare) and most were pretty plain "boy's rifles." You can be entering pretty rarified air if you start talking with the Stevens freaks, but it sure can be fun too. My first Favorite got me into a small collection of boy's rifles. Not nearly as spendy a passtime as collecting, say, 19th century schuetzen rifles.
Check the bore! If it looks crudded up, ask that it be cleaned so you can see what you're getting. Check the total function of the action. Test fire if possible. It would have to be a pretty pristine and early Favorite for me to be thinking about parting with $500. I don't think I've paid as much as $400. Talking about a good tight shooter here, not a perfect specimen.