re shorts – i've started doing triathlon and use triathlon shorts – they are designed for swimming aswell, so have a very thin chamois. I can't believe how good they are for both running and biking, as well as not feeling like you have a soggy nappy round your nethers when swimming!!
in the past when i've done duathlons, i've just done them in my bike shorts though and it's been fine.
prob wont make much difference whether you do road or off road, as a first timer i'd prob not have my sights any higher than just having a good time and learning – see what other people do. don't forget as well as going from run to bike, you often have to go back to run.
practice your transitions in both directions, and talc in shoes is brilliant!!