Take a look at a used Sig P239 if you can find one. It should be in your price range and it is one of the Sigs that was tested by the DHS and passed. It is large in profile, but fairly slender with its single stacked magazine. Here's a summary of the DHS testing:
In the 2004 DHS tests, various SIGs, HKs, Glocks, S&Ws, Berettas, and XDs (w/o grip safety) were tested in 9+P/40/357. Beretta withdrew early on, leaving 5 makers to complete the tests. Over 3 million rounds were fired through over 300 pistols.
Tests like accuracy, reliability, durability, drop (mag and gun), sand, plugged bbl.
Toughest requirement was consistency.
To get a contract, all your guns had to pass all tests in all models and calibers. SIG and HK were the only makers to do it. The others failed at least one test w one model or caliber.