Yes you can have multiple profiles which work on all games.
Miranda, the Mario Party game is quite like the Wii games which are party like - you can get others along these lines.
What's quite clever with the switch is that it comes with two "Joy cons". These can be used either as tiny standalone mini controllers with limited controls, which are fine for games designed predominantly for multiplayer, like Mario Party, Mario Kart, or you click two joycons together into one adapter and it is used like a full sized controller and has a few more buttons on it, for more complicated games.
You can buy more sets of joycons, we have two sets, so we have two full controllers or 4x mini controllers for party games. I'd recommend this for a family of 3-4 or maybe even one set of extra joycons + a full controller which can't be split in half (these are a bit cheaper).
It's quite similar to how on the Wii sometimes you use the wiimote + nunchuck and sometimes you just use the wiimote on its side, like a controller. Except instead of the nunchucks being useless on their own, it's like you have 2x wiimote type controllers.
The joycons also slide into the side of the Switch itself, which charges them and means that when you take the Switch out of the dock it acts as a handheld console.
The only issue with the joycons is after a while the analog sticks start leaning to one side, but you can send them to Nintendo and they repair them and send them back. Or maybe they have fixed this with newer ones?