You are very near two larger grocery stores. Just go out the gate on the roadside and to your right, you will walk right into a pink grocery store. Just kittykorner to it, is another.
You can easily walk it on the beach too. Go out to the beach and turn left, head north and immediately after the Blue Tang Inn, turn left again. Go up the little street and again, you will walk to the pink supermarket with the other market kittykorner to it.
I never bothered with delivery. I'd just load up a couple of bags of whatever I needed for a day or two, and walk back home with it. Certainly from where you will be located, carrying your own should not a problem at all.
They are both good stores. Sometimes the produce is better in one than the other. I couldn't quite figure that out, since I thought all fresh produce arrived on the same day, but whatever.
You can buy liquor and beer there too. The pink market even had a nice Chilean Cabernet Sauvignon, that I didn't think was all that bad considering.