Our 1st cruise in 99 we booked thru a local travel agency which sat down with us and arranged everything. It was nice! I think the 1st time you may want to do that. Ask all the questions you can. Write them down and bring the list with you!
Our last cruise we booked via orbitz.com. Their prices were OK and we didn't research alot and just booked early. No problems whatsoever and if I had a question I just called their 800 number and they were very polite and knowledgable.
Our next cruise (March 2004) I booked by doing ALOT of research. Called about 5 local TA's, looked on orbitz, expedia, travelocity, cruiseonly, cruisequick, you name it I looked for prices
...but we ended up with bestpricecruise.com as they beat any price I found online and with the local TA's.
I think it's what you feel most comfortable with. I think now that I've gone on 2 cruises already I feel more comfortable researching on my own. If it's your first one you may want to get the personalized attention!