As everyone else has said, extra joy cons are a must.
My 3 dc share a switch. To begin with, I bought:
Switch plus mariokart 8 (package)
Extra set of joy cons
And a couple of cheaper games (crayola scoot which is fun, but not proper multi player, Lego Harry Potter and Lego city undercover - the Lego games are good value with lots of gameplay, IMO)
The switch comes with everything needed to connect to tv.
Do set it up beforehand - you’ll doubtless need a system update, plus I’ve always found it a good idea to have some knowledge of the game/gameplay so that you’re not scrabbling around trying to sort it out while cooking lunch, making sure only rubbish goes in the bin, the lost of presents is updated for thank you letters, etc. Plus system setup needs an account etc. You might want to look into an online gameplay account - depends on what games you want, or how you want to play them. I got away with not having inline membership for a couple,of,years, but as my dc have used it more, and acquired more varied games, it became more necessary.
Animal Rossini is fully playable by multiple players - not as a full multiplayer game though. The primary account is the residents rep (on our switch, this is me to sidestep any arguments between dc ), but when ds wants to play, he signs in from his player account, and he can do everything. The multiplayer set up gets a bit annoying, although it is easy enough to switch leader to have different players doing different bits.
Our most played games are:
Mariokart
Mario party
Animal crossing
Pokemon (lets go and sword/shield)
Just Dance
Lego games (now have Harry Potter, city, Jurassic world and Lego Worlds)