Ruger or Buck Mark semi is almost certainly your best choice. Right in your price range and you'll never be ashamed that you bought either.
It's getting damn near impossible to find a decent .22 revolver at the $300 price point. The used H&R's maybe, but I've heard nothing but nightmare stories about the Taurus 94. Think I heard the Tracker might be better though. You'll only find a used Smith .22 revolver if you find a widow/sucker and have loose morals.
Hated the 22A when I shot it - felt cheap and unnatural in my hand, some folks swear by it. Lots of folks think their Walther is the neatest toy ever, but quite a few remark on "Pop can" accuracy being about its limit. Don't know too much personally about the NEOS or Sigs. Hear pros and cons on each, but the good and bad seem balanced.