I have 3 of these same ones, the cheaper white plastic variety. I have an acrylic shower and they hold great. Tile might work as long as the cups line up without crossing a grout joint.

One thing you have to remember to do, pull them off about twice a month, clean the wall where they were stuck and the suction cup as well as the back of the suction cup with the lever open. I left one of mine for about 6 months and it had a nasty dark stain that took me a few weeks of cleaning with a bleach cleaner and melamine foam sponge.

My wife is nearing 80 and she really appreciates these. I have one just inside the door, one almost in the corner and the third above the level of the built in seat.

As well as these I use a good plastic shower matt with suction cups on it and a piece of non-slip stuff, I think it's part of one of those rubbery waffle pattern things to keep rugs from sliding around. She uses this on the seat to sit on so she doesn't slip off.

Get a good rug and place it outside the the shower to step on to.