I second the Henry. Fun to have. Cheap to shoot.Are you looking to buy a new rifle or a used one? If you're looking for a new rifle I would go with a Henry .22 lever repeater. They're light-weight, inexpensive, and fun to plink with.
Personally I would buy a used Marlin 39a. They'll set you back a little more than a new Henry, depending on condition. I've owned two Marlin 39a's and there isn't one thing I can say that I didn't like about them. Cheap and fun to shoot. You can find them made between the 50's to the 90's, and they were made very tough, top quality.
As far as where to buy... check ingo classifieds, I have seen some on here. You can check auction listings too.
Also I wanted to add: I used to stand at 50 yards and hit a 6 inch steel plate 19 times in a row with my 39a (thats how many rounds of LR the tube holds). Nothing brings a smile to your face like the sound of the lever then the *ting*.
The Henry stands up to heavy use far better than Marlin. We shoot approximately 1,500 rounds in one day through Henry lever action 22s every year at the Karl Kelly Conservation Officer's Youth Camp. The same rifles are used for Hunter Ed classes, 4-H Instructor classes, Hunter Ed Instructor Classes and Women in the Outdoors classes all year totaling over 2,000 rounds a year through the rifles. The Marlins have feed issues under heavy use.
I have to take issue with those 'blanket' statements. I've put well into the mid six-figures (at least!) of assorted .22 RF ammo through my Marlin 39M over the past 30-odd years, many times going well over 3,000 rds. between thorough cleanings with no feeding issues whatever. Putting two or three bricks through it in a single range day with my nephews and/or friends has been commonplace.
Nothing has broken nor worn out to date, and it just keeps getting slicker with age.
Not knocking the Henrys. They're relatively inexpensive, readily available and I've heard nothing but good things about their customer service. They're certainly better made than most all of the old original Erma Werke model they decended from I've seen over the years were. And I can see where these factors would play a large part when choosing something for a program such as the one you've described.
But I would like to see a Henry which has seen as many rds. through it over as many years as my Marlin that's held up any better.