You need very Specific Answers - not generalizations..
"Buy Local" mqy be generally good suggestion - but depending on the charter base, you really need info from folks who have been at your SPECIFIC charter base in order to get meaningful recommendations. Make sure the posters have been to your location when evaluating their suggestions.....what makes sense for Road Town may be meaningless if the advice is based on a Guadaloupe charter experience.
We have chartered twice from Tortola (Road Town, and Hodges Creek Marina).
Both times, we pre-ordered lots from Bobbies - for stuff that you might not need to check personaly for quality (hard goods, booze, drinks, etc.)....and then went to the store in person to select the stuff we wanted to "approve" (eg: certain produce and meat cuts).
This is generally cheaper and better selection (if you are picky) than allowing Sunsail/Moorings/whatever to pick your food for you.
So.....from TWO charters of personal experience from TORTOLA - I can suggest that you buy most stuff from a pre-order to Bobbies (google them for an order form), and buy the remainder in person.......if you want to pay MORE, and don't mind someone picking out your stuff (perhaps with slightly less pickiness than you might do....) then pay the charter company to stock you totally (not my preference).
Paul