I wouldn't worry about the components till you find the right frame. You want something comfortable and well built that is a material that is going to be comfortable for commuting. Aluminum gives a harsher ride, carbon is awesome for soaking up the road but I wouldn't want to commute in traffic with carbon, steel would be my favorite of them all but cheap steel is heavy and not as lively.

Once you figure out the frame you want to go with a reasonable parts build that isn't too flashy considering this is a commuter.

Next you want to spend a lot more money on locking your bike and watch some videos from people like Hal Ruzal so you don't get another bike stolen. This probably should have been at number 1

For a complete bike the Cinelli Gazzetta seems like a good bet. It is not fancy but it is a good starting point from which to improve. I would swap pedals for SPD compatible ones and switch the tires to Gatorskins but that would probably be it for a commuter/beater bike. However small things people wouldn't easily notice could be changed for something nicer.