I have a beach cottage and started with BM White Dove. Even though it looked great in my own residence, it was too dingy looking in the smaller rooms of our cottage. After doing some experimenting, we were thrilled with BM's Decorator's White - it looked crisp, clean and went beautifully with navy and red accent colors. Hope that helps.

I don't have a suggestion about the white paint color, but wanted to make another suggestion. I have a basement done in a similar color scheme. Only, I painted just the one wall with a patio door that looks out on the lake dark blue. The other three walls are white. I like that the one accent wall becomes the focal point of the room. It frames the view nicely, and the other three white walls keep the room bright and light. You may have other reasons for painting two opposing walls dark blue, I just thought I would propose another option that might work for you.