I generally go shopping the day I arrive, stock up on gouda, bagels, wine, etc. that covers most of my stay. I'm usually in a Studio as well. I've used Super Foods mostly in the past, but someone above recommended Ling's as having had a major refit and looking better than ever, so I may try them again this year -- we used to use Ling's regularly for years, but at some point switched to Super Foods.
I'm not a picky eater -- though I'm a vegetarian -- so that's a short list, and left to myself, I'd probably eat at Marmok or Champions (now called something else) and maybe Casa Tua if I'm up for a longer walk. Oh, and Hostaria, because their food is just so well done and it's again walking distance --via the beach -- from the Marriotts. My travel companion(s) like to try different places, so I've gotten to visit a few other places, but when in Aruba I rarely travel further south than Oranjestad, though we did eat lunch at Charlie's way down south once, and that was . . . interesting.
I do wish for a real sidewalk on LG Smith from the resort south, as the beach walk is sometimes . . . circuitous in practice, esp. after imbibing, but it's all good, and my un-egged beer is more than satisfactory, if you get the reference.
I'm at the Ocean Club the first or second week in Dec. every year. If you hear singing and guitar on the beach 4:30-6pm, that's us.