Since you mentioned the range, competition, and home defense, here are my picks in your price range:
CZ75 SP-01 or SP-01 Phantom
Springfield XD Tactical
Smith & Wesson M&P 9mm PRO Series 5-inch
The Browning Hi-Power, Sig P229 or P226, and the Beretta 92 would also serve you well if you find them more to your liking.
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