There are so many ways to go here, hard to choose.

I am not a fan of a vessel sink for everyday use. Please research this.

What colors are thinking about?

First, what is your budget? Next, what style do they want? Next what are their favorite colors.

General advise: 1)Paint the trim around the window white. 2)Add white 6" baseboards.

Oh yes, I forgot to add that, I'm definitely investing in a new sink-vanity, mirror, paint, or wallpaper.

white and some shades of navy blue, black accents.

We have the Scandinavian style in mind

The flooring tile should be white or marble. Depending on the budget, I'd recommend 12x24 tile peel and stick or porcelain tile after tearing out the current floor. Use the light wood vanity with vessel. Instead of using the small backsplash that comes with vanity, use a chevron marble or similar tile from baseboards to ceiling. If this is out of your budget, use wallpaper than looks similar. Because marble and wood have gold undertones, I'd go with champagne bronze pulls. Them blue mirror and bathroom accents. Some examples are below:

Thanks for the ideas!! I would definitely go with a light color floor and I love the bronze pulls.

I'm inclining for wallpaper, I need to find out if the sink/toilet wall is the one that it would be the correct one to accent or maybe just use white tile on that one and dark color in the rest of the walls.