You seem to have the same attitude and reasoning that I have about cycling. I was 41-ish, about 20 pounds overweight, driving 11 miles to work only to spend a large portion of my day driving around in a state vehicle. My idea of exercise was the time I spent climbing ladders and walking to and from my work truck. At 40 I'd been diagnosed with HBP so I initially turned to jogging. That was an off and on thing that proved to be too hard on my middle-aged joints and shins, so I turned to commuting. Hadn't been on a bike in roughly 20 years...but hey? I figured that if others are doing it, why can't I? So I tried it and fell in love. I've been at it for about a year now (not religiously) and have logged around 2,500 miles on my current bike.
Now although I biked all of last week, I still hitched a ride with a co-worker this morning. For me, I get wiped out after a whole week of commuting and my body just needs a break every so often. The trick is not to let it make you lazy so that you skip more than one day at a time. A few months back, that attitude snowballed into a three-week hiatus. Not good!
Anyhoo...good luck and have fun! Sounds like you're gonna fall in love with it.