One way of identifying white marble is color consistent. Meaning white marble might have Black vein.(Natural stone). If too many thick black vein the appearance will look bad. Not all white marble slab will be consistent in color.
Another way to identify best white marble is higher cost of each slab. I assume best marble will be high in cost.
Another way is to find a contractor who know white marble and knows what ideal for your house.
Top of my head Makrana is number one and I think it followed by Ambaji marble in India.
In our house I was going for a complete snow white marble look. But ended up with white marble with black vein. To keep the cost low, ended up with going Ambaji marble.
What I didn't know was that Ambaji white marble had 10 or 20 different varity or white marbles with different cost.(Most likely Makrana follow the same procedure) On internet I saw white Ambaji white marble as complete white with few black smudge marks which wasn't the case when I purchased it.
Family choice was marble because of low maintenace cost. Meaning don't have to replace tile.
My advice to you is to go with what is hottest trend in your area or at the moment.
Look into company called Kajaria who manufacture tile. In North America I saw Kajaria (India) tile being used in shopping mall, so I assume they are of high quality. The other point I like to make is Vitrified tile is the hottest thing in India. By the way I am not spokesman for Kajaria
Yes white color for flooring is excellent choice at the current moment.
The size of tile depends on the size of rooms.