Best budget setup you know of

My small-game hunting rig is a Hatsan 135 Vortex .22 with a Williams peep sight, front fiber-optic rod and rear iron sight removed. Makes a front ghost ring similar to target sights. Mine loves Crosman Domes above all else, and while it isn't a one-hole gun offhand (although it can be from a bench), it works well for up to rabbit-sized game out to 50 yards. That setup should leave you with $200-$300 left over.
If you want to use a scope, I would recommend the 155/150 Vortex in 22. Same velocity, but in a fixed-barrel underlever. Just be sure to get a tough scope (Mine has a Leapers mil-dot) and a one piece mount. The recoil on these things is no joke.