There is, or was, a distinction between "3 Gun" and "Multigun". The former requires the use of handgun, rifle, and shotgun, but they're shot separately, and the scores for the three guns are combined. Multigun can have the use of the guns combined on some or all of the stages, requiring transitioning among the three guns.
The scores of the multiple Courses of Fire, or "stages" are combined to determine the overall winner. So, the format of a 3 Gun match might be two stages shot with the rifle, two with the shotgun, and two with the handgun. A Multigun match might have you engaging targets with rifle and pistol on one stage, rifle and shotgun on another, rifle only on another, etc.
There are different competitive divisions, and which division you choose will determine what sort of gear you will use.
Most people shoot a 9mm handgun, .223 rifle, and 12ga shotgun.
Different sanctioning bodies have different mixes of equipment, so to an extent, you need to tailor your gear for the specific game.
When I shot USPSA Multigun, I shot in Limited division and Heavy Metal division. At that time neither Limited nor Heavy Metal allowed optics, so all of my guns had iron sights. Today, I don't think there are any competitions that don't allow at least non-magnified optics of some kind.
Some people will buy very specialized gear, while others, like me, take more of a "run what you brung" approach, shooting guns that you might already own.
I had a 12ga pump shotgun, a 1911 .45, and a M1 Garand, so I shot Heavy Metal division where those guns are legal, and appropriate. When I shot Limited, I substituted an AR or M1 Carbine for the rifle.
It's fun, but the price and availability of ammo today can make it hard to either assemble, or afford, all that's necessary.