Depends on how old the children are. If they are 15 and above, you may want them to maintain their own accounts and identity on the devices. Otherwise, you may want to be able to monitor what they put on their devices. It looks like a management problem, not a technical one.
You can set up your iDevices to either download purchases automatically or not. If you delete an app from one device, it has no effect on its presence on other devices.
The downside to using different apple IDs is that if there is an app you want on all of them, and you don't want to buy 4 copies of the same thing, then managing their installation and upgrades is a pain. You will have to sign out of their account, sign in with yours, download the app, sign out, and sing back in with original account. Repeat. Repeat.
If you set up all of them using your own apple ID, that means you will have to buy them any apps they want to put on their device. Unless you are comfortable giving them the password to your account on the iTMS and the credit card authorization that is attached to it. And you have to make sure not to set up iCloud sync, because then they will also get your reminders, calendar events, photo stream, and any iTunes music.