Find a club that has target matches. You'll want a good .38 for target work, namely a Smith & Wesson Model 14, or maybe even a .38 Special Auto pistol. In time you will want a .45 ACP target pistol so you can compete in all three categories. Clubs often sell reloads to their members at very attractive prices. You will likely end up reloading your own ammunition. There are three categories for bullseye competition: Rimfire, Centerfire, and .45 caliber.
If you continue you will probably want to stick with autoloaders, as there are stages for slow fire, timed fire, and rapid fire. In a club, you will find some of the nicest people on earth, all willing to help and encourage you in your endeavors. In addition, at the end of each year there is usually a dinner with awards presented and a general good time.
I was still in high school when I entered competition, used a Ruger Blackhawk .357 Magnum (With .38 Special wadcutters)for centerfire and a borrowed S&W K-22 Masterpiece to start out. My gun case was a taped-up shoe box, with cotton for ear plugs.
I worked up to Sharpshooter level by the winter of 1960 when the magnum vision appeared to me.
Bob Wright