I have a tile shower (tiles walls and tile floor). Where the floor and walls intersect, there is white caulking that had become mildewed. I need to replace the caulking, but want to be sure I use the correct caulk, the best product for a shower floor.

Any name brand tub and tile caulking that is mildew resistant.

Dap makes a shower caulk that contains a mildewcide built in, look for that at the home store. It's a bit stronger than just resistant to mildew, it kills it.

Ive always used silocone chalk. Why not use tile grout. Either or I suppose. Just remove ALL the old stuff

Grout is for flat wall surfaces but not for seams like in the corner or down at the floor. Those corner have just a tiny bit of flex to then and grout will just crack and fall out. Silicone caulk with mildewcide is the right way to go.

Ballagnerb1 if only I could spread some rep around id rate your answer. Lol your right grout doesn't do well in corners it always cracks, your suggestion is the best way to go.
You also may try some caulk remover for the old stuff, it worked for me the 1 time I used it.