Personally, that's what I'd do. I'd never upgrade from one OS to another, always best to have a clean start in my opinion. Bit of a pain configuring the new OS just how you like it, but worth it in the long run.
If your machine can run Mountain Lion it can run Mavericks too, you can create a USB installer with the 'Install Mavericks.app' that downloads, using the following command;
Code:
sudo /Applications/Install\ OS\ X\ Mavericks.app/Contents/Resources/createinstallmedia --volume /Volumes/Untitled --applicationpath /Applications/Install\ OS\ X\ Mavericks.app --nointeraction
(assuming your USB drive is called 'Untitled')
You could always try that, might avoid the issue of not booting from your DVD drive?