I have all tile on my first floor. Makes sense with dogs and living at the beach. But I hated mopping floors - I felt like I was just swishing dirty water around.
I purchased the Hoover Hard surface cleaner and it is wonderful! It squirts clean fluid on the floor like a carpet shampooer, swishes it around and then squeegies it up from the floor. My floors are actually clean and dry quickly.
That's great that you found a device that works for you because a whole floor of tile would be a lot of mopping, wringing and rinsing with a traditional mop. I used to mop my bathroom floors on my hands and knees with a towel because it was easier to me than using a mop...LOL!
I'm thinking about getting a steamer. When we bought our home, it was only 2 years old and inhabited for less than that. It was a bank repo. The people were not clean...they had dogs and evidently lots and lots of mice...BRAND NEW HOUSE! The bank hire two women and it took them a full week to clean. Then I cleaned after we bought it. DH thought I was nuts running a carpet cleaner again. Shudder. I found too much stuff in hard to reach corners.
I cleaned the grout in the floor tile twice. Once spraying with Fantastik and scrubbing with a long handled brush. The second time with a bleach cleaner and the same long handled brush. I betcha there's no telling what a steamer would pull out of that grout. Especially since we've now been here 9 years...no inside pets though!
I really do need to clean the grout. The kitchen and hallway were tiled when we built the house 13 years ago and the rest of the first floor was tiled about 7 years ago. I have heard that you should not use bleach on grout. Hoover makes a grout cleaner I plan to try soon. Mine needs to be resealed so we just might get a pro to come in and redo it.