That should depend entirely on what type of gun you want to shoot. There is a class of competition for just about any gun.
Are you talking rifle, shotgun or pistol ?
Off the top of my head, I think that precision .22 would be a good place to start for rifle, with a moderately customized Ruger 10/22.. you could probly get into it for aroun $4-500.
For shotgun Try Sporting Clays, A GREAT gun would be the Bretta AL390, around $6-700, but you could shoot very well with a Mosberg semi-auto for several hundred less.
For handgun, if you get a Glock you can compete in the GSSF matches held all around the country, they are great for beginners. For the cost of any decent self-defense gun, a few 10 round mags, and some decent carry gear (holster & mag pounches) you can start IDPA.
Let us know more what you are looking for adn I'm sure that we can be of more help.
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-Essayons
