Does the thread count matter? Not to me, as long as the quality is good.
Air-conditioned or ceiling fans? A/C in the bedroom is a must. Anywhere else is a bonus.
Internet access? A must.
Ocean view from a hill? Definitely, unless you plan to slash your rental price to match the lack of view.
Number of bedrooms? 2 is good.
King-size beds or Queen? I prefer a king, but I can live with a true queen, but not a full/double masquerading as a queen. Stuffing two singles together? Just no.
Bathtub or Showers? Shower. A bathtub is a waste of water.
Maid service daily or every other day? Daily, with Sundays and Holidays off works. I can get by just fine with every other day when renting as a 1BR.

I've rented many, many villas since I sold my place on the French side. "Thinking" my way through a few of my favorites, here are some of the things which I found to be either Must Haves, Nice To Haves, or just Nice Touches:

A decent sound system with outside speakers and a Sonos box (internet radio, smartphone app, stream your own music) is nice to have (but cranking the volume and rocking the 'hood isn't cool).
A hammock is very nice to have.
An icemaker is nice to have, but only if the filters are changed on a regular basis.
A shady place to read - I read a lot when I'm on vacation.
A safe large enough to store an iPad Pro or a laptop.
Adapter plugs so that both European and US guests can plug into outlets. Most (all?) "power bricks" and "wall worts" are multi-voltage these days, so a transformer shouldn't be necessary for guests.
Access to a washer and dryer is a major plus, but not a requirement.
If there is satellite TV, which I would rarely watch, US satellite TV such as Dish Network.
A reasonable selection of cookware/utensils/glassware/dinner ware/basic spices (I'll settle for salt and cheap pepper grinder) such that I can do basic cooking/entertaining for 6 people (I once rented a villa on St Barth which had no corkscrew!) Plan on breakage, so buy for more than 6.
Toaster, coffeemaker
A hairdryer which actually dries hair
A list of important phone numbers such as villa manager, emergency numbers such as fire/police, perhaps a list of favorite restaurants
Kleenex!
I'm reaching here, but a wi-fi printer which I could use to print boarding passes, including from an iOS device
A makeup mirror.
A "leftovers" drawer, for leftover sunscreen and bug stuff - invaluable when you forget to pack one your own.
Another drawer for reusable shopping bags.
Sufficient hangers in the closet. Even better, more than sufficient so that I don't have to borrow from the 2nd bedroom.