One of the new sheet flooring products that lay unattached might be a good choice. Many are very durable.

NOTHING beats tile for a beach house. Sand residue ground in by feet will quickly erode the finish of any vinyl floor and wood won't stand up that long either. You might get 3 years out of vinyl and 5 out of wood before needing to replace or refinish.

Not accurate in my opinion. There are many vinyl floor choices that can last decades. I installed vinyl flooring in heavy use homes and many of those floor coverings are still in service twenty years later. As with any manufactured product, you usually get what you pay for. If you buy low on the price point scale, you usually get a product that is poorly engineered and cheaply made. Sheet flooring, whether virgin vinyl or some other similar raw material, can be an excellent flooring choice.

I concur with vinyl lasting the longest and you can find nice varieties out there.

Well, I kinda have to agree with the tile being the "best" choice here. They use sand to remove paint on metal, and it will surely remove the finish off of vinyl or wood. Walking on a floor with sandy feel is a sure recipe for sandblasting down the finish of anything pretty rapidly. You would need to practice a "sand containment system" if you chose anything but ceramic or porcelain.

The beach house we rented for a week had an exterior foot wash. and we used it, and left our shoes at the door. We still managed to track in an unbelievable amount of sand. It just stuck to everything and was very fine, like sugar. It got everywhere too. Even the master bath, which was furthest from the door, had a bit of a grit coating by the end of our stay just from us changing bathing suits there. If I lived there full time, I'd have wanted a vac pan in every room.

Something cheap so it is not expensive to replace.

I grew up on a beach. Tile, stone, or concrete are the only floors that will stand the test of time when it comes to sand. Using anything else will be an exercise in sacrificial flooring.