If you're interested in competition, drive up to the Pima Pistol Club (near Catalina) on any Sunday morning. There are IPSC (USPSA) matches on the 1st and 3rd Sunday, a steel combat match (speed shoot) on the 2nd Sunday, and IDPA on the 4th Sunday.
All these start at 9 AM. Lots of people there would be glad to answer questions, describe/explain what's going on, and generally show you the ropes. Once you get a feel for it, jump in and give it a try. Almost nobody wins the first time out. Many have shot for years without winning and still come back. It's a lot of fun if you like to burn up ammo.