Yes you do need a passport & $20.00 for immigration to Virgin Gorda. We went on Pirates Penny (sister to Stormy Petrol) in July. It was a beautiful trip & I would highly recommend it. The fee was $110..00pp. It was an all day trip with snorkeling, going through the baths, lunch at Cooper Island Beach Club and more snorkeling.
Since we were staying in St. John, we left from Cruz Bay. But I think they dock in Red Hook.

You do NOT need a passport to go to Virgin Gorda or any of the British Virgin Islands. What you do need is proof of US Citizenship. If you have a CERTIFIED copy of your birth certificate (usually they have a raised seal) and a picture id like a drivers license, that is sufficient. We did trips to Jost Van Dyke and Virgin Gorda in April and again last month without passports. They are not necessary. An argument could be made that it is more convenient to have them but they are positively NOT required.

You really do not need a passport but it is easier if you already have one (only one document to carry around). We just took our first trip to the Baths aboard the Limnos out of Red Hook, St. Thomas. Would really liked to have spent more time at BVI but enjoyed it none the less. The Limnos is a power catamaran so it is quick but loud (deisel smell also). We prefer the relaxation of a nice sail boat such as the New Horizons due to the distances involved you need a powerboat to get to BVI. If you want a day sail check out New Horizons out of Sapphire Marina near Red Hook.