Minimum partition size for normal osx usage?
You're on the right track with 9-10GB if you're doing a barebones OS X install.  See the OS X Mavericks requirements. However...

If you're keeping the root /Applications on the same volume as the OS, then you might want to leave additional space if you plan on adding applications to the system.  I've never tried to store /Applications on a separate volume from /System (the OS) and /Library (system-wide preferences, support files, etc.), but might be worth a shot if you have time to experiment.  

My only concern would be disconnects between core OS X applications and their supporting frameworks.  A prime example would be something like "DVD Player."