I used to compete in three gun, even won 33.33% of a national championship, heh.
There are different organizations with different rules for the guns, equipment, and ammo. Do you want to buy lowest-common-denominator equipment to shoot with more organizations? Or do you already have something and you want to find out who you can shoot with?
The basic guns would be an AR-15, an autoloading shotgun, and a high-capacity pistol. Pistol cartridge depends on the rules, 9mm or .40. Add a low-power optic to the rifle to shoot in Tactical or Open division, a bipod to shoot in Open. Speedloaders for the shotgun to shoot in Open, or belt stackers for other divisions. Holster depends on the division and pistol. You'd need a locking race holster for an Open gun, but anything else can use something like an Uncle Mike's molded. One or two rifle magazine pouches. Several pistol magazine pouches. Velcro inner/outer belt system, maybe even two outer belts for configuring for different gun combos. The Safariland clip-on dealio might be the way to go for that now.
If you want to shoot a .45 1911, pump gun, .308, or something similarly uncompetitive you shoot look at the Heavy Metal division.
You should go to a match and see what people are using.