Looks like you are getting good suggestions: touring or cross bike; TREK type hybrid - flat bar.
My bike to work is about 16 miles, and I make it longer going home to avoid so many stop signs. I'm only biking to work once or twice a week when there's no ice.
I'm using a highly modified (component-wise) circa 1990 Rockhopper.
I recommend going with racks. I don't get the cycling with a backpack at all.
Fenders are great. Why in the world would you want to get wet from above AND below while you're riding? That's crazy! Just take the clean stuff from above!
Anyway, what you want to do is totally do-able. The first time bike-commute back & forth will be the hardest. Each time it gets twice as easy.... or half as hard. I'm not sure, but whatever. The first time for me was the hardest.
cheers