My #1 recommendation is NO YOUTUBE, unless it's for education purposes. I don't have the App installed on any of my kids devices (they can access it via the website, but they don't do that). It's just a cesspool of garbage for kids. Even YouTube Kids is bad. Occasionally, they will complain about not having the YouTube app... but I never took it away, so they aren't missing it.
I've loaded up the iPad with fun age appropriate games and activities, that don't require any In-App purchases. If my kids want more apps, then Apple will ask my permission on my iPhone.
I use an Ubiquiti Dream Machine as my home router, so I have some basic content filtering and I have some categorisation of the traffic available, but nothing detailed.
In terms of video games, my recommendation is have a games console in the living room. They have access to video games, but they can play them where everyone can observe. They can have their own video games, this isn't a problem. Microsoft sends me a family report every week about what games were played, but I don't pay much attention to it. Purchases require parent approval on Xbox too.
With a 0.2 and 2 year old, you are somewhat lucky. The ages are close enough that they will play with each other a lot... and screen time won't be too much of an issue until they hit teenage years.
Good luck.