If low cost is a concern, and you can go with a single-shot, look at an NEF Handi-Rifle or Ultra-Varmit(?) Surprisingly accurate, and only $200-$250.
I had my Ultra at the range today, and she was shooting consistent groups just over an inch at 200 yards (handloads with Nosler bullets--but she does pretty well with the 45gr. Winchester "value' varmit loads.)