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I agree. The OP, cdahl said, "This gun would just be for fun, target shooting, etc. I don’t plan on carrying it."
To me, that means a fun gun to show off and enjoy, not a working man's tool. If you're choosing between a plain-Jane Sierra 1500 and a drop-top Corvette, which are you considering more for fun and which is more for work? Don't get me wrong. I enjoy ripping all Hell through the dirt and mud every once in a while, too but, that's not what a work truck is for. And it sure isn't what a Corvette is for. In case it isn't obvious, Ruger = work truck and S&W = sports car.
I'd also ask if you plan to reload or strictly use off-the-shelf ammo. If you're reloading, maybe you can come up with that perfect mellow, accurate, and fun .357 load for your gun and budget. If you're strictly buying boxed ammo, the choices for light, accurate and easy on the budget get real slim.
Like mcb said, the .38Special is a fine, accurate, easy on the budget and very fun cartridge in a K/L-Frame Smith&Wesson or a E/I-Frame - or even a good D-Frame - Colt's revolver. The Model 10 Classic is an elegant, simple weapon you will never be ashamed to bring to the range. Ditto for a Colt's Official Police or Police Positive Special. Not many revolver chamberings are more accurate than the .32S&W Long - except maybe the .22LR. Also good choices.
If you're fixed on a 586 or 686, get the one that looks sharpest and fits your hand best. It's for fun, not work. And start reloading if you don't already so you can make some pleasant-shooting target loads.