Cool, pleased to know you've thought of that stuff. The Switch is a looooovely device, one of my favourite toys, and I've got all the consoles stretching back to 1998 or so, most of them still hooked up.
The Switch can be used entirely on the telly, cable-tie it into the dock it comes with if you want to avoid having DS wielding it carelessly. The two controller "ears" can be used for two players on most games, or put together with a grippy thing (that comes with it) to make an approximation of a normal controller for one player.
You can also buy the "Pro controller" which is a normal one, so then you can have one person using the dual-ears and one on the pro controller. Budget another £60 for it though... another pair of ears plus a holder is £70+£30 though, even worse.
There are loads of great games in the £2-£20 range, but the big deal Nintendo ones (Mario Kart, Zelda - Breath of the Wild, Mario Odyssey etc) tend towards £50.
You have the choice of buying those high-end games on physical cartridge (like a triple-thick SD card), in which case you can sell them on later but on the downside they can be lost/eaten by a toddler, or by downloading them from the Nintendo eshop (on the Switch itself or on the website). The cheaper games are usually only on download.
After a dozen download games or so you'll need to buy a microSD card (128gig=£20=about sixty more games) to hold more.
The game prices vary, but there's usually a sale on. I recently got the download of Mario Kart for £30, but it's back up at £50 now.
There's a huge range of games from huge open worlds to explore (eg Zelda BOTW, Xenoblade, Okami) to arcade adventures (Mario Odyssey, Lego Incredibles) to tight claustrophobic platforming (Celeste, Hollow Knight) to happy bouncy platforming (Rayman, New Super Mario Bros, soon Mario Maker) to life stories (Stardew Valley, Moonlighter) to gorgeous arty things (Gris, Gorogoa) to shooty bang bang (Bangai-O, Doom, Wolfenstein) to indie stories (Undertale, Desert Child, Golf Story, too many more to mention!), there's something for everyone. Many more than what I've mentioned for most types of game. Hit up "best of" lists on the Internet and read reviews on Eurogamer and the like.