Quick update: The school I was helping only had OneDrive for business, so that's not available for Moodle - pity...
I think Google Drive might be best next thing, as it's free (as in 'you-are-the-product-not-the-customer'-free), gives 15Gb and most crucially is easy & accessible from Moodle, Office 365, iPads, other tablets, etc.
And to clear up my thinking from above, the 'repository' is not a 'repository' at all. It's easier for me to think of it as a protocol which enables students 1 2 and 3 in Moodle to connect to their own GDrives/Dropboxes/etc. 1 2 and 3 via this protocol in the File-picker etc. Students set up their [GDrive] accounts outside of Moodle, and then come into moodle and enter their [GDrive] credentials to make the link to their personal repositories ...
Thanks all