That depends on the game- Ridge Racer 7, for example, has no voice chat at all. Resistance, meanwhile, does have chat in a lobby before games and during play.
If you have it the USB headset made for the PlayStation 2 will work fine. If you don't want to be messing with being connected to your PS3 with a cable, however, most bluetooth headsets made for cel phones work too- they just need to be "paired" wih the system (done in the Settings menu).