First handgun

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.

I think a .22lr would be suitable for squirrel hunting. (I think)

I have a Ruger MK. II and it's great fun to shoot. The cost of .22 is also a big plus because when I shoot I really go through the ammo. It was my first handgun and you can find one for about $240 or less. Ten round capacity and styled somewhat like a Luger. I can't really recommend another gun because I don't know whats a suitable caliber for squirrel.

Check out the S&W 617, 10 shot model .22. Excellent quality, almost same fit as a 686.

Bob

The 617 seems very heavy to me. Woudl try some of the other suggestions first. Buckmark works well for me as well as the Smith mod 17

I would recomend something in .22LR , for simplicity I would also recomend a revolver.

Here are some good .22LR pistols
Ruger MK II or III , Browning Buck, Ruger Single Six convertable, Ruger Bearcat,Ruger SP101,Taurus 970,Taurus 94,
Smith&Wesson 317, Smith&Wesson 617

As uglydog said, the S&W mdl. 41 is very accurate and the .22 lr round is cheap and a good squirrel round.
However, I don't think you will find one for less than $600, unless you buy used. (IF you can find one!)

I have one and it'll NEVER be sold.

I'd also suggest the S&W .22 lr revolvers or the D. Wesson .22 lr revolvers.
Accurate and will fall under your self-imposed price limit.

Keith