current OLED version, it's great and should be compatible with games for quite a while.

It comes with 2 joycons, so your boys can play together, but if you wanted to join in, you would need to get more or get a pro controller (which I would much prefer).

Tons of good games, do a google search of good switch games and get some that look like your boys would like them. Also ask them what they like to play if they play at their friends house, they should probably have some in mind if they are asking for it. Any mario game is great.

Peripherals can wait, you will decide what sounds cool or fun after playing for a bit, things like steering wheels or sports peripherals are popular.

The switch comes with a dock that will connect to any HDMI monitor or TV.

Yes, you can open it early and connect to internet as it will require an initial OS download. Each game will want a download of various sizes the first time you play, so you could insert each game and start the download, though they usually don't take very long.

It's a very fun system, and you may find yourself playing with it when you can steal it away from the kids.

EDIT: I forgot memory cards, get at least a 128 gb one, doesn't need to be anything fast. You may also want to look into a charging bank for on the go.