For IDPA/USPSA get a glock 34 or glock 17 which is a 9MM or an M&P 9mm. They are the most popular gun run in IDPA.
http://www.aafgidpa.com/admin/equpment_survey.htm. I would go to a range and rent each first, I try not to be buy a gun I have never shot before. Kind of like not buying a car you haven't seen in person.
Glock 17 used should be between $400 to $500 are easy to maintain, and there is a youtube vid to do almost any custom thing you want to do to them.
The first upgrade I would make after shooting a couple matches would be some new sights like the warren tactical fiber optic front and plain rear set.
My first IDPA match they had every new shooter evaluated they could function the pistol controls and the shooter didn't sweep themselves drawing from a holster, other clubs I shot had no evalulation. Your going to need at least 5 mags, but I started with just 3 mags, new mags are $25.00, you can probably find used mag at half that which will be fine since it just for gaming and not CCW. For your first match you gonna need a holster, stay away from soft nylon holsters that collapse easy, I would start with an inexpensive fobus or safariland holster.