Lots of people use large porcelain slabs, Corian slabs, or modern shower wall systems to avoid grout. Still not as popular as tile, although more folks go for darker options to hide the inevitable discoloration.

#2 is a ludicrous question. There are thousands, at all quality and price levels. Just do a search in the Shop section of this very start to see if you like anything there. But the kind you get from a cabinet place are fine too.

I am redoing a bathroom now so I will add my input based on current design decisions.

1. I am using small tile (about 2") for the floor because it is easier to lay with sloped contour to the shower drain. Avoid white grout. It will not stay white (at least the way I clean). Pick a darker grout for a better look overall. All of these were recommended by my contractor. Don't forget to seal the grout.

2. Regarding vanities, look on line and see what you like. The recent trend seems to be to get something that looks like furniture and has space on each side and below. I opted for wall to wall so as to maximize storage space. I also selected a vanity with a standard toe kick (like kitchen cabinets) because I don't want to clean underneath. My wall to wall dimension is 70" I picked a 66" vanity and will fill in and color match the 2" on each side. I am having a custom countertop made so it will go wall to wall.

I will add my choices . I like 12 x24 porcelain tile for both bathroom floors and shower walls with a smaller tile same material for shower floor . I use a matching grout never white and that keeps grout lines to a min. gives a nice clean simple look that allows a choice of awall color and accents , like towels etc done the road . I will say I aslo relly like a good quality shower pan instead of a tiled floor in the shower . I am not sure what your issues were with grout but I find a darker grout but not black works well .