I re-downloaded the Mavericks installer and re-made my USB stick before doing a complete re-install. Within 5 minutes of booting, things started crashing. Flash installer crashed on every attempt to load, as did Dropbox installer. Safari did it now and again, and then the freezing started. Crash logs show windowmanager crashing, and then it references the graphics drivers.
I've come to the conclusion my GTS 450 is the issue, so I'm currently reinstalling Mountain Lion
Thank you everyone who has helped me with this in the last few days. I hope you all manage to get your own issues sorted out. I'll be back with mavericks when I can afford to get some new kit, or when someone comes up with a definite fix