is it best to do it yourself online, call the resort or use a travel agent to book a trip to t&c?

That's a very wide open question, however, it does pay to shop around. You might get a great rate online today and not so good tomorrow. It you are comfortable on the net, that might work for you but you are the one doing all the research. If you use a travel agent, they do the research for you.
Personally, I use the internet wherever possible.
www.destinationcaribbean.net allows you to do everything from the one website, ie hotel, flights, cruises, etc. Might work for you.

As bajangirl said, if you're comfortable doing some legwork online, you should be able to book your own. The resorts all have websites. Although once you've narrowed down your resort choice, it is worth a shot to call them and find out if they have any specials that may not be on their website.

Personally, I would only use a travel agent if my itinerary is complicated.

Thanks for your help!

I think half the fun of vacations is planning and booking them myself. I love researching new places...