I recommended the MKIII 22/45 above since I have one, but since revolvers are now under consideration, I concur with the Heritage recommendation...have one of those too! I think you might have a hard time finding a Single-Six used within your budget, and obviously new is much more. Another used revolver option to consider is one of the High Standard revolvers (Sentinel and Double-Nine are two models). They are single/double action with nine round cylinders. You should be able to get one between $200 to $300.
A different option would be the Phoenix HP22A Rangemaster Kit. You get a 3" and 5" barrel in a semi-automatic pistol and other goodies in a nice storage case. You should be able to find the entire kit for less than $250. They have a pretty good reputation as long as you stay away from extreme high velocity ammo. I plan on getting one of these when I can find one in my area.