I appear to have written an essay 😁 please take what you like and leave the rest as they say.
How old are your DC?
I am now very pro switch and (considered, supervised) gaming. My experience is from getting the Switch, Minecraft and Animal Crossing for my then 6yo in early 2020 with next to no idea of what I was getting into. I quickly realised a second switch was needed for a second child in the family which I'll explain.
It seems as if the main cost is the Switch itself but after a while you may find you spend a lot on games, extra memory and subscriptions. When I compare the theoretical cost of after school childcare one day a week for a term or a couple of family days out including meals I'm in the right ballpark for the cost of enjoying Nintendo as a hobby. It doesn't make it affordable just a way of thinking about the value!
If you're not into gaming, as I wasn't at all, you might think of it as indoor play equipment like a swing or trampoline is outdoors. A one off purchase, taking turns and sharing will be fine. It can be more like a bike and trainers though. Ideally everyone needs their own and they'll get to know the feel of the steering, trainers will mould to their individual feet. Learning to use a joycon (several buttons, motion control and a joystick) really well takes practice and, for example when fishing in Animal Crossing, there is real motor skill involved not just pushing a button. (When you get to Zelda, Subnautica and Cuphead...)
All this makes it extremely valuable and fun and there's a ton of different learning opportunities, exercise and the chance to be creative. Gamebuilder Garage, brilliant Lego games, Just Dance, Ringfit.
I can't imagine a situation where it would be better to have a Switch lite. If you can't take a big plunge and get 3 Switches I'd suggest considering getting two - one for the 'kids' and one for the 'grownups' so they can share as much as possible eg Mario party - good for 4 players as long as you have 4 joycons - but you can let one child 'borrow' the grownups switch at times. In the long run if everyone takes off with it you could get a third and then allocate one to each child. If not you have more flexibility with 2 switches than 3 switch lites in my opinion.
You can put several profiles on each Switch so whichever one they are using each person has their own profile to play on.
I'd also seriously suggest you buy the 'grownups' one as soon as possible and start using it. It will be worth knowing how it works - you're the battery that will make it go at Christmas, you need to know how it works and how the games work. You could all have a wonderful time but that might depend on being able to deal with frustrations quickly.
There are really beautiful worlds to explore - Zelda Breath of the Wild for example - and fantastic music, YouTube has some great orchestral concerts of game music.
If course you may know a lot of this already. Happy gaming 🎮