I have basketweave tiles in my bathroom - floor and shower floor as they are NOT slippery at all because of the grout. I love my floors :-).

I absolutely didn't want anything slippery when I remodeled as I had 12" x 12" vinyl tiles in my pre-remodel bathroom and any bit of damp made them slippery.

I rented an apartment during my remodel and the shower had 12" x 12" marble tiles in the shower and on the bathroom floor. I considered that to be the bathroom of death because it was so slippery that I was afraid to move my feet while showering and had to make sure I never touched the surface of the floor after a shower.

Since you are rightfully concerned with safety do not neglect GRAB BARS. These need to be installed when you are constructing the bathroom as they have to be attached to the studs for safety so they don't pull out when used. They have styles now that aren't institutional looking - mine are oiled rubbed bronze to match the rest of my fixtures. I really like having that extra bit of security even though the shower floor itself is NOT slippery with the small marble tiles.

I would advise you to go to the top of this page and type "Marble tile shower" into the search box. Chose "In Bathrooms" or "in Advice" for where to search. Read about the issues of marble tile shower floors before you commit to this choice.

...and then go shopping for marble-look, porcelain hex tiles.