If you're buying a bike specifically for commuting, why not buy a bike designed with that purpose in mind?
A mountain bike is pointlessly heavy and over-specced for the job. A fixie will be light and simple, but unless you're used to riding one in traffic, it might not be for you. Riding one up and down hills takes nerve and/or experience and/or fitness.
Why not buy a commuter bike? You can always go hard-core and trade it for a fixie later.