I don't think anyone has mentioned this, but talk to your wife about it. Ask her if she minds the extra time (assuming your not spending extra gym time). If she's cool with it, than absolutely start riding. It's also a great way to learn your new area better.

As for doing triathlons, realize training for that will be way more time consuming than just commuting to work. However, I would absolutely recommend a road bike, or something hybrid-esque, for a 12 mile commute.