Honed or brushed stone will generally be less slippery than polished stone.

Be sure the stone you choose is not soft. I have durango limestone on two bathroom floors which is beautiful but on the softer end of the scale so it has developed a couple cracks here and there over the years.

Interesting about the limestone cracking. I read that limestone is softer so travertine might be the better way to go.

Get a sample tile, place it on the floor and step on it with a wet foot.

Travertine around pools can be quite slick, even honed.