Love the Switch. I’ve had one for 5 years. The nice thing about the Switch is you can buy the physical small cartridges and insert them into the console, or you can download the games all digitally. You will want to get a MicroSD card if you go the digital route. I have both digital and physical games so it’s a mix of the two routes.
Here are my recommendations:
Mario Kart 8 (multi-player)
Smash Bros Ultimate (multi-player)
Super Mario Odyssey (1-player)
Lego Star Wars: Skywalker Saga (1-2–player game; if they like Legos or Lego Movies they’ll love it)
Zelda: Breath of the Wild (1-player game; my favorite game overall; for the 9y/o, or for you when they’re asleep!)
Minecraft (don’t have this game but lots of kids love it)
Sonic Frontiers (also don’t have this but have heard awesome things)
Donkey Kong Tropical Freeze
Lastly, you could ask them what looks cool to them - more action fighting games or more story mode/role playing games.