For a short commute of 1 mile, nothing special is required and who cares about speed? I'd think you could pick up a "clunker" for pretty cheap that would be adequate.

A fellow randonneur uses an old beast he found at the side of the road and built up into a cheap commuter. Put a rack on the back. There are pannier/backpacks available.

Make sure you can fit fenders if you're in less than desert weather. Check out the variety of commuting bikes these guys and gals use.