You've got options. Nintendo controllers, old controllers, third-party controllers. Let's break it down.
The Official Stuff
Joy-Con 2: Comes with the console. Magnetic attachment, mouse mode, GameChat button. The new standard.
Switch 2 Pro Controller: Full-size, $80, has everything. HD Rumble 2, motion controls, amiibo, back buttons, headphone jack. Worth it if you play docked a lot.
GameCube Controller: Nintendo makes one specifically for Switch 2. Great for the GameCube classics library.
Your Old Joy-Cons: They still work! Just wirelessly though. They won't snap onto the sides. Keep them around for games that need the IR Motion Camera.
Your Old Pro Controller: Also works. Pairs wirelessly or plugs into the dock. Can't wake the console from sleep, but otherwise fine.
Third-Party Options
Basically any Bluetooth controller works. PC gamepads, phone controllers, whatever. Go to Settings, Controllers & Sensors, Change Grip/Order, put your controller in pairing mode, done.
Pro tip: if Joy-Con drift annoys you, look for controllers with Hall Effect sensors. They use magnets instead of the parts that wear out. No drift.
How Many Can Connect?
Eight controllers max. That's theoretical though. The actual limit depends on which types you're using and what features they're running.
Multiplayer Setup
Mix and match freely. Someone on old Joy-Cons, someone on a Pro Controller, someone on a third-party pad. It all works together.