Thought I'd post a message for the record for anybody else searching for how to get Debris running under WINE. I downloaded Debris last night and got it installed on my machine that runs Linux Mint 4.0 Daryna Main Edition. This distro is Ubuntu-based, so this should also apply to Ubuntu 7.10.
WINE 0.9.46 is the installed version; the only tweak that I had to make was to set the Windows version as Vista to convince Debris to load past the title screen.
Anyway, it runs nicely, saves the output without problem and only makes me wish for a native Linux version even more :P
As such, I cannot suggest much in the way of tips, as it worked so smoothly for me.
I'd suggest that other WINE users also post their experiences here for the record