If you're talking on the iPad itself, you can't disable the notification badge (when it appears - it's direct from Apple). All you can do is ignore it.
In iTunes, you can turn off the notification box pop-up. If there is an update available, you will get the pop-up. Before you reject it (that's the important part!), there's a box you can tick to say "don't remind/ask me again." I don't remember exactly what it says - it was so long ago that I told iTunes this ... and I can't find a setting to do it outside of that pop-up box.
The most important thing is to read all the pop-ups iTunes throws at you. They're sneaky and usually, the default is to accept whatever iTunes/Apple wants you to do. Ya just gotta be vigilant!
Hope this helps.