My advice is not to sweat it too much.

Based on the wealth of information available on this forum and in other places it's easy to come to the conclusion that commuting by bike is a lot more complicated than it really is. Six miles is not so long that there's really a horrible choice as far as bikes are concerned. Most people who commute in all weather like to put fenders on their bikes, and some bikes are easier to get fenders for than others so that's a good question to ask the bike salesperson.

Go to a bike shop in the area you'll be riding in. There are forums for different regions so you might want to ask in there for a bike shop recommendation. If you post your location, you could ask here too. There are shops that cater more to commuters than others.

Test riding a few different bikes is a great idea. You'll have many choices with your budget.