I like being able to run a fatter tire on my commuter than on my road bike. It adds some comfort and it can add (depending on the kind of tires you get) a lot of flat protection. Plus I like eyelets for a rack and fender.
I think it's tough to beat a vintage bike you pick up from CL for a commuter.
There's a heck of a lot to choose from (road or vintage mtb) and the price is right. Your best bet price wise tends to be a vintage mtb. They're cheap, well made, and ride pretty well once you throw on slicks. I like vintage road bikes as well but they tend to be more expensive than mtbs.
The point is that it's a lot of fun personalizing your commuter and the build process will get you motivated to get out there and commute.
I grew up in New Orleans. The weather certainly won't stop you from commuting in terms of the cold. There is some great riding in the Feliciana Parishes.