I would say a single speed road bike would probably make you happy (doesn't have to be fixed, probably best if it isn't). It already sounds like that's what you want. From there, determine the frame material you want and what options you care about, like fenders, racks, etc and how much you want to spend. Then you could probably narrow it down to 3 or so bikes pretty easily.

But all you said really was "faster", so then you should get this . . .