Don't get caught up in cost of the console or the games. What's most important is buying a console they'll actually play with titles that are age appropriate.
Growing up, I went from Atari to NES to Genesis to Playstation to Dreamcast to Xbox 360 to Xbox Launch to Xbox One S...I still own the last 3 consoles. I got the kids a few titles like Minecraft and Rush (Pixar game) some cheap ones off the marketplace. They like playing Minecraft, but most other games just aren't age appropriate and my 6 year old has gotten more frustrated than anything trying to learn Minecraft.
On my Xbox One setup, I have 1 Xbox account and then 3 guests. I use that one Xbox account for Xbox Live and to buy all my digital content like games (not counting minecraft coins that follow the minecraft player). That allows my kids to sign in on one Xbox with my account and the other Xbox is my "Home Xbox", so it gets all the titles I own by default. That's how we can buy 1 digital title and have 1 Live account and play multiplayer between systems. I mention that because the Xbox One system is solid and pretty cheap compared to other options....it just lacks titles if the kids are under 10.
I'm going to break down and get them a Switch. There are often $15 digital titles. I still don't know what's best on Switch...Digital or Physical. (based on when they go mobile with it) I really don't want them on it all the time, so I'm just a little reluctant to get it. I just don't know what other big ticket items to get and I know it's one of those things that I need to order sooner rather than later knowing the way inventory has been lately.