I was in the same spot as you a few years ago. I'm overweight too, somewhat. Not sure what your weight is or should be. Anyway, I wanted to commute to work, but I thought the distance of 14-15 miles was too far. Then I got my first road bike and decided to try it. Luckily it took me less time than I thought it would, anywhere from 65-85 minutes depending on wind largely, and other weather conditions. My route is quite hilly, lots of ups and downs in both directions.

I'm still overweight and I'm still slow (sucky eating habits and heart condition to blame, in part), but I still manage to commute 2 or sometimes even 3 times a week. Give it a try! I do think cycling-specific clothes are a must for this distance, for me anyway. Also we have a shower at the office. My road bike is outfitted with a rear rack and trunk bag. I've ridden my heavy utility bike but it's much slower.