Filling big horizontal gaps in bathroom tile
Grey, sanded. 'black' is easy: #60 charcoal. 

I'd grout it first though. I've had luck with a grout line that wide, and it was a wood-to-tile threshold nonetheless. A 1/2"-plus deep and ~2" wide? I'd go for it; that will seal the gap better too. Then base and quarter round.

I'm an all-or-nothing type of guy, but that's way too much all to get excited about what will end up being a slightly too wide grout line along the trim, of an otherwise serviceable tile job. - When you gut the bathroom though....