I am not positive, but I think it would work better to tile the shower now and tackle the floor later.

Yes, you can do that. I did exactly that in one bathroom, except that it had a tub which I changed to a shower, a year after the floor was tiled.

Catbuilder, thanks so much for the verification!

I haven't done this, but I have tiled a couple of bathroom floors and I think that you should lay out the tile so that any cuts are at the shower, just in case you have to remove them to get the old stall out, also in case the new tiled shower is deeper. Of course you don't want to end up with small cuts at the back wall of the new shower stall (or even worse, at the curb!) so plan the layout very carefully. Good luck.