Grout and a matte tile finish will ensure any shower floor to be "non slip" Even a glossy floor can be that in a mosaic with grout.

All showers should have grab bars, very stylish varieties are available. I would consider a larger opening than 36 inches if possible, and make every attempt to use the SAME product on the bathroom floor as IN the shower. A very skilled set of pros for all execution of the project, along with a consultation/design with someone very experienced with ADA compliant design. That is your very best investment.

only products laboratory tested, can ensure no slippage. good housekeeping provides these services. Nothing in a box store will be guaranteed in this perspective, no matter what the material is. products need to be specialized, we have a lot of experience in this arena.

For safety compliance, there should be no glass shower doors, a low lip shower pan, handheld, bench seat, and durable base. Also has mentioned above grab bars, outside the shower and inside.

even a tub cut will work