Well, I now have an embryonic website. And I've got to grips with the document structure (actually, it makes a lot of sense to me). User access permissions seem to be more configurable than the default state in Joomla.
Unfortunately my Ubuntu laptop threw a wobbly this morning while I was editing menus, and that had the effect of damaging the database. Had a bit of trouble repairing the damage, but all seems to be well now.
Which of course brings with it the question of backing up the website. I can't see an obvious way to do that (other than manually copying the files and exporting the database via PHPMyAdmin). Guess a spot of Googling is in order! On the other hand, the University requires I stick to a defined set of modules, so this may be an issue...
I've selected a relatively plain theme, and will set about tarting it up a bit. Personally, I prefer quite spacious and essentially white web page design, so I may stick with that - and it'll be easier to edit the CSS file to make it "brand compliant".