There are excellent provisioning options in St Thomas (Plaza Extra, Cost-U-Less, and Pueblo which is closer to downtown) and you will save on provisioning costs. However, I think it's not worth the bother if you are on a 1-2 week charter.

To maximize time on the water, I would provision from Riteway or Bobby's while the boat is still at the charter company dock. Have the provisions delivered or have some crewmembers provision while you're doing the boat checkout.

If you come to STT, you'll either have to pay for dockage or schlep provisions to the boat by dinghy. You'll also have to clear in to C&I in Cruz Bay or Charlotte Amalie, which you can bypass if you want to head straight to SVI (will need to clear in there).