I haven't stayed in any of these places, but I've visited them all. They're all okay. Xanadu is small and rather unusual in design, and if I remember correctly it does not have a pool, but the other two do. Casa Caribe has more of a condo/residential atmosphere, and Caribe Island has more of a full-service small resort atmosphere. I think the decision you need to make first is whether you want to be in a more "remote" area (Casa Caribe, which is on North Ambergris Caye, accessible only by water taxi or ferry) or whether you would rather be on the main part of the island, albeit both Xanadu and Caribe Island are a couple of miles south of town, so you'll need to take a taxi or golf cart (or bike) into town.
As to jewelry and such, there's no need to take it because there's really no place to wear it on a laid-back Caribbean island. And it's true that if you leave an expensive camera or watch out, someone just might be tempted to pick it up (just as anywhere in the U.S.), but in general the island is safe and crime is not a factor for tourists -- indeed 99% of visitors probably feel far safer than they would in many popular Caribbean island destinations such as the US Virgin Islands.
As to the sea, in most places the water is quite shallow close to shore. The places you are considering are several miles from town and there is relatively little boat traffic, and the water is clean. Of the three places you mention, I'd say Xanadu is near the best beach, Mar de Tumbo.
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