Here are the 3 most popular pistol competitons.
http://www.uspsa.org/
http://www.idpa.com/
http://steelchallenge.com/
Here are some great videos that discuss each of them.
http://www.youtube.com/watch?v=jXbdbHReqQ8
http://www.youtube.com/watch?v=eFDaVIbJ4AU
http://www.youtube.com/watch?v=z4RXNo4gEyk
You can use all kinds of guns for these sports. Some of the most reasonably priced and popular guns are the Glock 17, 22, 34, or 35. The S&W M&P 9, 9L, 9Pro, 40 or the new 40 Pro.
Holsters and mag pouches from Bladetech, CompTac, or Kytac are very popular in all of the sports. Let me know if you need further assistance.