what’s the best way to regularly clean a kitchen floor with grout?

Vinegar and water does a good job. It is a degreaser & kills germs. Just mopping with plain water alone gets about 99% of the bacteria.

I’m going to buy a spin mop for my kitchen & bathroom floors. Have been using a bar mop towel & spraying it down with white vinegar & water and cleaning on my hands & knees but sometimes my back isn’t feeling so good & I need an easier way. Should be really quick with a spin mop.

Yes, steam mop. They clean well, doesn't require chemicals, dries quickly. I used one when I lived in Arizona and almost all of the floors are tiled.

Get it as clean as clean as you can and then seal it. That will help prevent it from getting dirty.