The grout doesn't have to be dark to set off the white tile. I think it looks best with a very pale grey. We went with the 2" hex, but wish we had gone with 1" or smaller just because it would hide the dirt better with more grout lines. If you do a search for jejvtr's pictures she has the 1" hex. Ours with the 2" before the threshold was installed

I always like to use diagonal pattern tile, but with a border such that is appears to have a "rug" look. Sometimes I create a border around the diagonal "rug" pattern with accent border tile that matches the accent border tile around a shower or vanity. Also, I like to have a somewhat similar tile pattern style with all bathrooms of the residence to tie in the look. When I see bathrooms of a residence with totally different style of tile is seems less coordinated to me. I've used different material for different bathrooms of a residence, but try to have some kind of similar pattern to tie them together. As for the size of tile, assuming the floor is perfectly flat, larger tile is proportionally better for larger floor areas. Usually 10\\\\\\\-13 inch tile size is a good proportion for most average bathroom sizes. Small power rooms can go with smaller size tile and maintain appealing proportion to the floor space. If you have a threshold between areas of the bathroom, consider a matching accent border tile on the floor that separates the two areas. Here is a photo of bathroom with "small" style pattern for a floor space that seems too big for it... bathroom still looks great overall.

Sumod- The medicine cabinets are simple wood frames with a cabinet-grade plywood back that just sit in the stud cavity. Because of the dimensions, the front of the frame projects about 1"+ beyond the finished wall. The medicine cabinet doors are also plywood with veneered edges and they are attached to the frame with standard cabinet hinges (Euro hinges). The mirrors are just 1/4" plate glass ordered to size from a glass shop and held in place with mirror mastic and a metal strip at the bottom that you don't really see. The guy who did the cabinets just made the medicine cabinets as part of the job. I don't know about the door brand...we live in a large metro area that has lots of door shops and the doors are just solid core maple doors with the center cut out and a maple panel held in with molding. They're not stained; they simply have a couple coats of clear spray lacquer.

"We plan to use a whitish marble tile on the floor in this bathroom." Marble look ceramic? Real marble and kids is a recipe for etching, staining and slipping. Also make sure you have something with slip-resistance suitable for bathrooms.