In general, the older (geologically) the island, the more beaches it will have. Thus, Kauai has the most beach area of any of the principal islands. It's also less populated than Oahu, Maui, or the Big Island, so it's easy to find uncrowded beaches. Kauai also doesn't have the night life scenes of the other islands. So my suggestion would be Kauai.
But if you want to take chilling to an extreme, Molokai is a possibility. There is almost nothing to do on Molokai except hang out on a beach, and the population is small. The times that we have been on west Molokai beaches, we have been the only people present - on a beach that stretches for miles.
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With that said, I would suggest that you rent for your first stays and check out various areas or resorts. Then you can decide if you want to purchase or just continue renting. Personally, if we were starting on our vacationing journey now instead of 18 years ago, I wouldn't buy a single timeshare. The internet has made the rental market much more attractive and affordable.