I shoot on my school's 3 gun team so I'll give you a run down of what gear I use.
1 x double pistol mag carrier (though I do keep a 4th magazine in a pocket just in case); that gives me 52 rounds before I have to reach into a pocket
1 x AR mag carrier. Generally, you will never need more than 30 rifle rounds on a stage so I don't usually need the backup. However, in the event of malfunctions it is good to have. There have been two instances where I have used an additional mag carrier, but that was when there was a high round count on a stage. You can get by with just one and use a pocket if need be.
I have 5 x Glock magazines and 8 x AR magazines. Do I need all of them? No. How many would I recommend? 4 of each.
1 x dump pouch
2 x AP Customs 4x4 shell carriers, 1 x Man Mountain Engineering 4 shell carrier, I also have (4) 3 shell carriers. For shotgun reloading, these are a must if you get serious in the sport. Bandoleers are good for holding shells, but bad for reloading quickly. You can get by your first match or two with a dump pouch and bandoleer, but you need to be able to separate buckshot, slugs, and birdshot and know where each are in your setup.
1 x rifle sling
1 x good pistol holster (Safariland ALS is a good holster for 3 gun, but you don't always need the extra retention)
Are you wanting recommendations for a pistol?
***And a good 2-piece belt!