So I managed to install live Ubuntu on a DVD (eventually)
What do you mean with "install"? All you need to do, is burn the ISO to the DVD.
trouble is, I'm not entirely sure whether I can install bitcoin core directly on it (the dependencies won't write correctly will they)?
I haven't tried. But it means you'll need to give the live OS access to write to your hard drive, which is possible, but goes against the idea of using a live OS.
Anyway, I was wondering, before I go to the effort of installing Ubuntu, is there a faser operating system (also, I can use the same block database i already have on Windows that hasn't fully synced yet can't I)? My block database is a year and a half behind on its db.
I'm using Mint, but Ubuntu should be about the same. If you have enough RAM for file cache (12 GB works much faster than 4 GB), and if possible put your chainstate directory on a SSD, it'll be quite fast. Much faster than what I've read from Windows users.