If I was looking for a carry gun in 9mm and was limited to $300-350 I'd go with a Taurus PT111 Milennium Pro hands down. I own many handguns from a low end Charles Daly 1911, to several mid-level handguns (including a CZ and a Ruger) to two higher end SIGs- my Taurus PT140 Milennium Pro (the .40S&W version) can run with all of them being the equal to most, better than some, and not that far from the best. It has been 100% reliable through 750 rounds (most of them various JHPs- WWB, Magtech, Speer Gold Dot, Remington), it is accurate (though some people take some time to get used to it and get the accuracy), it has a very smooth DA revolver-like DAO trigger, it seems very well made and it was inexpensive. Mine was $350 out the door (incl. taxes and fee for the background check), some people report them for $290-300 in their areas.
If you aren't interested in the Milennium Pros, there are other options in your range. If you want a .380 my Bersa has been reliable and they can be had for just over $200 in some areas still (around here they start around $250 now). The Ruger P95 is a bit big for carry but is a decent gun and isn't much over $350. The S&W SW9VE (formerly the SIGMA) is now a pretty good gun, but stay away from used (they used to be pretty bad and I don't know how to tell if the gun is from before or after the improvements). Taurus has a few good autos (PT 911, PT 92) that depending upon prices in your area might work for you (around here they run about $100 over your limit) and the PT 911 isn't a bad size for carry. Still, I'd probably go with the Taurus Milennium Pro.