Tiling instead of baseboard in the bathroom

I've always torn out the sheetrock and put up backer board. Mastic on sheetrock is crap.

That's purely a personal aesthetics thing. My master has 18" tile. I'd go larger rather than smaller (but 18" is a little over). Larger is easier and looks better, IMO.

That's an old wives tale. Like almost old wives tales, it's partially true, depends on circumstances not mentioned, and almost always admits of a previous failure that would undermine any building system.

Or larger is gregarious and hideous.

Backer board? Whatever.

My wall is just plain sheetrock. For the first room I did, I used Liquid Nails with tape to hold the tile in place 'til the glue sets. I used mastic on the second room. I don't think the tile cares much...

As to height, artistically, I suppose, the height should in proportion to the room size but in keeping with the function. How tall was the baseboard you removed? My observation is that 3" is way too short.

I used 6" for a bath in that it was convenient to cut the tiles in half, but whatever looks good to you. You might survey existing public bathrooms (YMCA, McDonalds, etc.) to see what seems appropriate.

I have 100s of feet of tile baseboard. It is all on the sheetrock. It is all stuck on with plain thinset. "Modified thinset" is only good for the store selling it at many times the $0.10 per pound price of regular thinset. IMO, YMMV and I don't care if it does. ____________

How high do you want it? IOW, it doesn't matter as long as it looks good to you.