The Western Nevada Pistol League meets every first weekend of the month. Their website is http://wnpl.org/
I frequent the "USPSA Lite" meets, which are VERY beginner friendly. $10 to play, usualy goes from 9am to 12pm. 4 bay with different target setups: cardboard , metal knockdowns. As far as gun choice, you can shoot just about anything you like. From a .22, to a Desert Eagle- or a .357 revolver- I've seen them all there.
Check them out, or come to a meet. The place is the Washoe County Range off of Pyramid Hwy. Take Pryamid Hxy North out of Reno, towards Spanish Springs. Pass Rangeland Road and grass Valley Rd- then turn left onto gravel where you see the sign for Washoe County Range. Follow the gravel road to the main covered shooting area, then turn right and follow the gravel road to a secondary shooting area (past the sign that says authorized people only) Park, and register in the largest building.