That was like my old commute ... I mostly used my converted mtb, SUB, using fenders, rack and panniers. I also had used my road bike a few times, with backpack. I preferred the SUB because of the road debris (better tires); more gears (7 mile climb); more fenders (lot's of rain).

My current commute is now 6 miles and better surfaces, so I road bike primarily.

Good luck.