Sorry for the late reply.
Color-wise it looks fine, as well as design-wise. It's very good in those regards. As far as the shading is concerned, it doesn't look very "official." Here's a very quick example of how I'd handle the shading:
Using the colors / outline in the original piece and colored using a mouse, so it's not 100% accurate to how I'd handle it, but it's a good example of the overall placement/style and a way to do the shadows. (Plus I had to darken parts of it to make the outline workable, so ignore the all-black parts.) Compare your version with this, and you can see the difference in shading. Try using more fluid lines instead of the sporadic circle shading if you're going for Sugimori-style.
I hope that helped! If you have any questions, send me a Note - I'll see it easier that way.
Microsoft Paint would likely not work as it doesn't allow for transparent backgrounds (as far as I know). You could do Sugimori-style art with it but it would be significantly more difficult.
Other programs should be able to do what I described in the guide, but I'm not 100% sure as I've never used other programs to make Sugimori-style art.