tri vs. road bike

Tri.  But if you're brand new to the sport, my recommendation is to ride with what you've got (road, mountain, anything) for the first season to see if you really like triathlon/duathlon.  A decent entry-level tri-bike with fitting is going to set you back $1500 and you have to ask yourself if you want to drop that kind of green for a sport that you don't know if you'll become addicted to.

And for the record, my stable consists of two road bikes, one tri bike and one mountain bike.