First off, DON’T GET A SWITCH LITE! The Switch is infamous for controller failure, like the 5200. It is not easily fixable and you would most likely need to buy new controllers. The Lite uses the same controller design as the Switch Joy-Cons do, so it’ll only last about 8 or so months (how long it lasted for me) before starting to “drift”. Nintendo is currently getting sued over this.
If you get a Switch, get a Pro Controller or, if you don’t mind, wired controllers. They are much cheaper than constantly replacing the Joy-Cons. The wired ones are only about $20, but the Pro is a bit more. It won’t work too well for on the go gaming, but they are definitely worth having around for a way to at least play the games in some capacity.
As for “family style” games, Nintendo has your back. Might I recommend Luigi’s Mansion 3 for you and your wife to play together? That’s very fun in co-op. Mario Odyssey, not so much. Great game, but terrible multiplayer.
If you are looking for a cheap co-op game, might I recommend Untitled Goose Game? I bought it on launch; love those feathery pigs and was super hyped to have a game based on them. It recently got a coop update, and my sister and I are loving it. The game is only about $20. Must have.
And sadly, yes, you do need a paid online subscription. Switch Online’s service isn’t as good as the PS4’s or XBOX’s, but it’s only $20 a year. It’s worth it for the free SNES and NES games you get. You can also play Super Mario 35 (while it’s out) and Tetris 99, among others with peeps online.
And I have heard the new Animal Crossing is fun, too. Haven’t played it yet, but I played a TON of AC: New Leaf for the 3DS and loved it. Still play it occasionally, and get sucked right back in!