As long as you use the same Apple ID on all devices, you can download the apps to all devices at the same time using automatic downloads.
On each iPad, go to Settings>iTunes and App Store>Automatic Downloads>Apps>On. When you download an app on one iPad, it will download to the others as well. You would probably only want to turn this on for the 3 iPads for the kids and keep it off on your iPad. You don't want their apps and they don't want yours, or so I would think. This would also mean that you would have to download the app on any one of the 3 iPads that the kids use and not use your iPad for this.
There is no way to keep the app arrangement consistent on all devices when you do this. If you download the apps in iTunes on your computer, place them in the folders where you want them and then sync the devices (one at a time) you can keep folder arrangement that way. There is no quick and easy way to do exactly what you want to do.
If each child has their in app settings - syncing them should not affect that. But if each child has their own data in then that's a different story.
Maybe a bit more background about the types of apps you are talking about might help.
