I would not totally be against other types of bikes. I started with road went to a cross & now Im on a 29er. I would not trade the Cadillac ride of my 29 for any of the other bike while commuting. Your commute is short enough most bikes will work fine.
Go to a good shop & ride different bikes. You should be able to stay beneath your $1000 limit. Get a frame of good quality & upgrade as you go. Disc brakes if you plan on riding in any weather & a frame that will accept at least 32 size tires. This can be a hard to impossible thing on a road bike. Fender & rack mounts can be a plus. However the distance you describe a pack might work for you.

Dont get so caught up with what to buy. No further than your going I would encourage you to go used then if this bug bites hard get a better bike once you know its something your going to stick with....Jeff