If punching paper is the main use consider 9mm. Ammo cost alone is reason enough, in a few months shooting you'll save enough money to pay for the gun. If your heart is set on a bigger hole I understand. Around here .40S&W was the most available round during the insanity, your area may differ.
I am an unabashed SIG fanboy. If you shop you should find a SIG in your price range. Here are a few models to check.
P220 Single stack .45 most common, 9mm used euro mag are out there. Full size frame
P226 Double stack 9mm, .40, .357sig, full size frame
P229 See above, midsize frame
P239 Single stack, 9mm, .40, .357sig, compact frame
These all come as DA/SA with decocker or as a DA only configuration.
Lots of German police turn in P6/P225 out there at bargain prices all are 9mm, same with P228 again turn ins but in a double stack 9mm. If you are willing to entertain a polymer gun check out a SIGpro 2220 2009 or 2340. A finer trigger you won't find. A real bargain too if they fit your hand, kinda chunky, but at <$500 you can't go wrong.