As others have said, you need the switch console (comes with one set of joycons) plus an extra set of joycons to enable everyone to play.
Last year I got a switch, plus Mariokart and the (then new) Pokemon game for £300. I know the switch this year has had a battery overhaul, so there won’t be much of a saving, but then the Mariokart game isn’t brand new so shouldn’t attract a premium...
Long winded way of saying you might find a better deal, but might not!
It can be worth looking at Very if you are a new customer, they often have a £30 off code.
My dc (and I) have loved the switch. Mariokart is amazing. I loved pokemon, but was a fan way back when! It’s not really a 2 player, though - you play to advance one person’s storyline, and the second player is literally a support role.
Just dance has been a surprise hit.
The Lego games have a good amount of gameplay - we have Lego Harry Potter and Lego city undercover. They can be two player (and need cooperation).
Carnival games has a shed load of mini fairground type games which are quite fun to play, but I’d wait to find it reduced (think I paid about £10 for it)
Zelda breath of the wild is absolutely stunning, but definitely single player and quite complex.
If you do go ahead and get one, then it’s fairly easy to pick up games in sales to keep interest up - not the main headline games, but there is a sale in the Nintendo Eshop regularly, and I’ve picked up all sorts, from really cheap (Astro bears - fun 4 player game which set me back all of 89p!) to classic board games like monopoly and risk (not the most exiting, admittedly, but fun to play in a new way) and classic games like Tetris.