Damaged iPad - what do I need to back up?
To be safe, run two backups.


First connect to iTunes and verify that "Encrypt Backup" (on the left) is checked. That will backup some private data that otherwise would be lost from the back up to your computer. Specifically, keychain and passwords, Health data on an iPhone.
Then try changing the password for the backups. This lets you know now that you can enter the password if/when prompted. If you can't change the password, delete the old backup and make a new encrypted backup to iTunes.
Lastly, put a clear piece of plastic over the screen and carefully go to Settings app and sign in to iCloud or go to iCloud and force a back up to iCloud. This is encrypted with the AppleID password and backs up passwords and health data as well as application data and settings.


There are things that do not back up like pairing records to trust specific computers, but those are by design and unlikely to be something you even want to back up if you could opt in to them.

Your SIM will transfer most likely (all Apple iPads are not carrier locked) and the store staff can assist you if you should need some carrier activation step. I would arrive early (at least 15 minutes) for the appt and expect to be there 45 minutes. That way if the store is slammed, you won't be surprised by a delay. Most stores have a caching server and fast internet, so you might stay longer to get an iCloud restore going if your internet is more tortoise than hare.

Lastly, I don't know if cellular data boost works during an iCloud restore, so I wouldn't put the SIM card in the iPad while iCloud restore was running if paying for that amount of data is unwelcome.