Mega dittoes on "anything in .22 RF". For inexpensive shooting, there really isn't much of anything in the same league, IMO. Finding any CF ammo - surplus, commercial, or even handloads - at a price per-round even mildly comparable to plain ol' generic .22 LR is pretty much a distant memory, I'm afraid. Sheesh!, with the prices for powder and caps anymore you can't even shoot a small-caliber muzzle loader as cheaply, even if you cast your own balls.
Virtually all action types are represented in at least a couple of flavors, in price ranges to suit any budget or taste from 'tap water' to Dom Perignon. It's really tough to find a quality-made .22, new or decent-condition used, that won't be capable of shooting better than most folks can hold for with at least a couple of loads and do it for a generation or two with moderate care. I don't believe that I've ever seen a .22 RF barrel on a rifle or handgun made in the past fifty years that's been 'worn out' from shooting, and that includes 'club' target rifles and handguns with documented logs showing round counts well into the six figures.
If you like playing with that pump shotgun, try a Taurus/Rossi M-62 or the like. 'Trombones' didn't rule the shooting galleries back-in-the-day for nuthin'!