If you don't yet have an AUP and you're effectively trying to draft one then I think you can start with big things - eg you mustn't use the laptop to do anything illegal or potentially illegal (so no torrents or P2P software) and you mustn't do anything which could bring the school into disrepute (so no porn, even if it's legal!)
Next big thing is that the user must not remove any software such as virus scanners etc, they mustn't turn off automatic updates and so on.
Is it reasonable to use the laptop for (say) booking a holiday, personal banking, shopping online etc? I think most people would say that's fine - it's unlikely to cause a problem or break the laptop. If something does go wrong with the laptop then it's easy to wipe and reinstall - the user won't lose anything (backup is a whole other can of worms, however)
What about iPlayer, Spotify and similar? Again, shouldn't cause a problem - they shouldn't stop the machine working and, if somehow they do then again it's a wipe and restore.
You're then looking at things which are reasonable but could cause problems - eg if I put all my personal digital photos on the laptop it's not really going to cause a problem unless I fill the disc or something goes wrong.
If the laptop goes wrong and I've got all my personal data on it then there's a potential problem - as a technician, I want to just wipe and restore the machine. As Joe User, I don't want to lose all my photos or whatever - this is where you need management backing to say that (say) users can store personal stuff on the machine but it's the user's responsibility to back this up to an external drive - the technician will repair the machine but is not responsible for recovering data.
I'd guess I can't ignore backup any longer :-) If the machine is being used for school work then it's likely to have stuff on it which does need to be saved if the machine goes wrong. I would expect to have a good backup system provided for the user which is as simple to use as possible and, ideally, reports back to the IT staff so that they know if the user data is not being backed up.
Ultimately, "reasonable" is one of those weasel words used by solicitors to keep them in business!
You could just set them up as network machines with VPN or access to a seperate partition for their work. Then they are an extension to your network and would come under the same rules... which brings us back to if you wouldn't do it in school... it isn't ok use.
We've just had a laptop come in the last few weeks. The hard-drive had failed. The teacher said well its got all my personal stuff on it. After explaing that he signed the 'AUP Form', that the only thing I can do is send off the hard-drive for a restore. The price came back at £690. I think he'll be backing up his personal data onto external devices in the future!!