RAM is more important than the processor, and of course it all depends a lot on what you want to do. If you turn off all eye candy, I think you could run GNOME/KDE pretty well on a ~300MHz processor, provided you have 128 MB of RAM. If you drop the desktop environment and use something like Blackbox, 32MB should be just enough to run one application process comfortably, but expect swapping if you try to multi-task.
Don't know what WINE requires - I would guess that taking the minimum requirements of your app under Windows and bumping it about 10-20% should be about right.