I have used WINE on Ubuntu in the past but it's generally easier to just run windoze. WINE will also not have the same graphics API that you would get with the latest versions of windows so you may not see performance increases even though ubuntu is easier on a computers resources. You may also be unable to use the 64bit version of the client even with a 64bit version of ubuntu running. If you are having problems with the client I would suggest checking the "use 32 bit client" in the settings menu.
If you are having issues getting the client to work properly I first of all suggest copying an install from a windows formatted drive where the client has already been installed. WoW is really great in this way as it is able to have the directory where it was installed copied and the game will still function, and not having to muck with getting the installer to run will likely remove some problems from getting it to work.
You can also head over to http://www.playonlinux.com/en/
they have basically done most of the legwork on getting games to install and run using WINE
My wife's laptop has two hdd's in it and one has linux installed. I have ran the wow client directly from the windows drive in ubuntu with WINE installed just by clicking the launcher.exe and it worked fine.