I haven't chartered there, but have spent quite a bit of time in the Grenadines on my own boat. It's a fantastic cruising area, and I'm sure you'll have a terrific time there. The locally-based charter companies are Sunsail, TMM and Barefoot in Blue Lagoon, St Vincent, and The Moorings, in Canouan. Canouan is right in the middle of the Grenadines, and easily accessible by American Eagle from San Juan. You can perhaps get some firsthand info on chartering in SVG at Traveltalkonline: Viewing forum: Charter Boat Reviews and Questions
The Tobago Cays is a must-do. There were no moorings there last time I was there two years ago, but may be now. See St Vincent & The Grenadines
for more info. The charter companies will probably have paid an annual fee for the yacht you charter.
Mustique requires you to use their moorings--check Doyles sailing guide for the latest. The moorings in Admiralty Harbour, Bequia, and Clifton Harbour, Union Island are "privately maintained", which means they may or may not be maintained. Be careful and dive on them to check for soundness. Last time I was there, moorings were $40 EC ($15 US) per night. You can anchor there--most cruisers do.
Have a great vacation. [aerial of the Tobago Cays]