In terms of simple
raw covering power, you'll get better results out of Vallejo Game Colour, and out of Reaper I cannot say. I would not recommend Vallejo Model Colour for the purpose of covering large areas with white. I also probably would not use Rackham simply for the sake of covering large areas en-masse with white either, more for careful detailing. Rackham can definitely cover, but the nature of it's binder just isn't as suited to covering large areas with speed. The Vallejo Game Colour product dries extremely rapidly so it's very good for quickly coating large areas. I think I would recommend Vallejo Game Colour the most since even though you will need to do more than a single coat, you can do coats extremely rapidly. You could also look at other manufacturers like Golden or Liquitex acrylics or Winsor & Newton's galeria series (cheaper series) of acrylic paints.
In my opinion however I think if you want to do a whole lot of white you should go get yourself a filbert-tip brush. Filbert brushes can be seen here:
http://www.dickblick.com/brushshapes/filbert/The large flat sides of the brush are perfect for covering large areas quickly, far better than using round brushes, and the rounded end is better than a perfect flat tip on miniatures since flat tips will tend to spread out over time if you're not supremely careful with them. That will make things go a whole lot faster no matter what brand you choose.
Of course I'm assuming that you *want* to cover a whole lot of area in a hurry to create a white basecoat after priming black. If that's not the case and you are just looking for spot-treatments of white, then what I said might not apply to you.