You'll need a rifle and a shotgun. ARs are the standard, but you can run a SKS or a Mini 14 or Benelli MR 1 or any other centerfire light cartridge (you could in theory run a m1a, but why handicap yourself THAT much)?
Shotguns can be pump or semi.
Forget the vest. Run everything from a belt. It's faster and allows more movement. Shotgun shells are also easier to carry and access, and in 3 gun, your shotgun reloading speed will and often times does make all the difference. Your mag pouches should be open at the top.
Personally, I run a pencil barrel AR for faster transitioning from target to target and easier to run around on the COF with (I'm lazy that way). You're not sending hundreds and hundreds of rounds downrange at a time, so heat build up and corresponding opening up of groups is a non event.
I also use a 870 pump for the shotgun in Canada, because I can use a +4 extension to get me to the 3gun legal maximum of 9 shells in the tube and still remain good with the Law. In the US, I run a semi because I can load that to the legal max without getting to be a guest of her Majesty's Prison