Do I need to set up individual Apple IDs for all my kids' iPads?
Solution 1:
I strongly recommend you keep a separate ID for each person. When buying a song, for instance, you can share among 5 authorized devices. My computer, iPad, iPod, and iPhone make four. Now that my wife and daughter have iPhones, and daughter, a MacBook, I glad they have their own accounts. No crazy apps I don't know about clogging my devices. You want your own apple ID and iCloud. Really.
Edit - Using your Apple ID for Apple services will help clarify the iTunes vs iCloud ID usage.
Solution 2:
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.
Solution 3:
I want to just answer the questions without making a recommendation since I can see many reasons that different people will want different account setups.
You can use one Apple ID for all the devices. If you want to turn off automatic download, you won't see the apps on your devices. If you delete the app from one device it does not delete it from the others. Even if you hide the purchase from your purchase history, the other devices can still re-download the app for free.
You only want to set up a second Apple ID if you want to let them control their purchases and budget (and not see their purchases in your purchase history). You can set restrictions to prevent age ratings and download blocks on a per-device limit and that is not tied to the Apple ID.
There is a limit where you will start having issues where more than 10 devices want to pull apps from one Apple ID, but even with 4 children devices, you still have 6 slots for yourself.
Solution 4:
Separate accounts with individual gift cards pre-loaded on each account might help teach the kids how to budget.