I shoot with a local club, primarily USPSA type shooting.
It is really fun, and a good opportunity to sharpen your skills as a shooter. Not many ranges let you move and shoot, shoot fast, and shoot multiple targets/steel.
I'm no expert, but I know a little about a lot if that makes sense. USPSA is broken down into classes, open, limited, production, etc. Personally I shoot production, which is basically a stock gun, you can replace basic parts like sights, but mags can only contain 10 rds.
This means more reloading, and no high speed ninja red dot speed shooting, but it's all relative when it comes to final scoring.
There is a balance between speed and accuracy, you can only move as fast as you can hit your target, so practice and muscle memory are key.
The club I shoot with has a practice night every week, which is scored, and also regular "trophy matches". You also learn a lot about legitimate formal competitions in your local area.
To start you will need a good gun belt, holster (USPSA requires the holster cover the trigger), mag holders, a gun (obviously), and at least 4 mags. We normally shoot a minimum of 3 stages, so I bring at least 100 rounds each practice night.
For example, I run a Glock 17 or 22, with a blackhawk serpa holster, double alpha belt, blackhawk mag holders, and 4 mags.
Just starting out, production is probably where you want to be. You don't want to go nuts and trick a gun out only to find out it doesnt work for you. Personally I like the challenge of running a stock gun.
I hope that helps!