I guess that for stitching ease and the final look, I would pick 16 or 18 count. Since it uses a lot of different colors of floss and all full stitches that will cover all of the fabric, I would choose the most available fabric and go with white. There is no point in using a colored fabric as you will be covering it with your stitches!
I like this pattern and they do make charts that are easy to follow. Just decide on how big you want it to be...look at the wall size as it might help you decide. I just think with all the colors that doing this in a higher count with tiny holes and squares, you might get tired!
Have fun!

I agree with Su to go with a 16 or 18 count fabric for fun and clarity. I also think that with the very dark edge corners (looks like black to me) the higher count is going to give you better fabric coverage, especially since I've read some reviews that some of DMC's black (310) and some of the other flosses recently (?) seem to be "thinner" in coverage.