Cheaper than Disney but more expensive than Publix or WalMart. If you have a car, I would go elsewhere. If you don't have a car the Hess is your best bet for beverages and snacks.
This link has a detailed entry with pics of the head station and prices. Keep in mind its from 2011 but it should give you a pretty good idea. It's from easywdw and Josh is great! We use his crowd calendar and its spot on too!
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I think the case of bottled water(24--16oz bottles) is between $5-$10. Some of the resorts are now selling bottled water, but you will pay $17 for the convenience of having 18--12oz bottles of water. I believe I've seen them at SS, BLT, and AKL, but they may be in more resort grocery stores. You can also get the gallons of water for about $3 at most of the DVC resorts. If you won't have a car, just take the DTD bus to Pleasure Island and walk across the street to the Hess Station. There is also a Hess Station across the street from BWV.
I personally wouldn't have Amazon deliver things. There have been too many stories of packages gone missing and having to pay to receive the packages in some Deluxe resorts. I think the Hess works fine for some things, although I don't think I would want to pack-mule a case of water and a 12-pack of beer back to my room.
If you are planning to stock up on a lot of items, you may want to check out the following:
Goodings also delivers to WDW Resorts, SoG, WBC and the Villas at Grand Cypress - http://www.goodingsdelivers.com/index.htm The supermarket itself is generally more expensive and they have a $25 delivery fee. I don't know how that stacks up with the other services.
We walked down to Hess this summer to pick up some yogurt beer bread and munchies and found the prices to be reasonable as compared to other on property Disney store prices. However the safety factor is I would only do it during the daylight because the sidewalks and near about the street in the distance crossing the street through Hesses parking lot is not pedestrian friendly
We're were just there last week. A case of Dasani Water was $5.99, a 12 pack of Yuengling beer was $12.99. I didn't notice the wine prices and they do sell small packs of diapers.