There are a number of handguns that would be suitable. I would look at the various Browning Buckmark models or the Ruger semi-autos. These are very accurate guns that are often used in competition, especially the Rugers. I have a S&W 41 and an old High Standard Supermatic Trophy Military which are the standards all others were compared to at one time. The High Standard is no longer made though they can be readily found on the used racks. Another good gun is the Colt Woodsman which is also no longer made. In revolvers I would look at the S&W 17, Ruger Single Six, and the hunting model from Taurus (sorry but I don't know the model name/number). Except for a new S&W 41, they should all be under your $600 dollr maximum. I would stick with the .22 LR chamberings as ammo is very inexpensive and accurate enough at handgun ranges.