Agree with Goldy. If you don't already have the Switch, that's the system to get primarily for the kids, and you can play most of the same games on it as you would on PlayStation and Xbox. We got several of the pro controllers and it's just like playing an Xbox or PlayStation. And while we mainly play it connected to the tv, the handheld ability is an added bonus and has come in real handy for roadtrips and baseball tournaments.
Let me throw this out there, too - I love my Xbox Series S. I was a PlayStation guy originally, but had a buddy of mine selling a Series S for $300 and took him up on it. It was a great buy. I'm the same in that I play mostly sports games (NBA, PGA, or MLB) and first-person shooters (Call of Duty and Halo mainly), and it's a great system for both of those. My boys love playing with me on the Xbox, too, though I think they enjoy the Switch more duet to having more games geared towards their ages.
EDIT: Oh! And one other bonus about the Switch is that if you do the Nintendo Switch online subscription, you get access to the old Nintendo gaming system apps, like Ninendo 64, SNES, NES, etc. Lots of the good old games on there, like MarioKart, Zelda: Ocarina of Time, Super Mario 64, Star Fox 64, Goldeneye, etc. I have it on my to do list to go through Ocarina of Time again. It was one of my favorite games growing up.