While I love the look of stained wood shutters... they wouldn't match our house. So I choose to paint ours white. I painted each of the pieces separately before assembling. It would be difficult to keep the paint off the louver pins otherwise, which would violate one of the most important rules of this step which is to maintain smooth movement of the louvers.
I choose to use a pure white interior semi gloss paint, which is fairly common for trim work. I found that three coats gave the desired look. I did this by hand with a brush, but some suggest using a sprayer. I imagine this would be much faster. I admit that the painting took me nearly as long as all the other steps combined. :( There really isn't anything tricky to this step. Just time consuming.
My daughter has expressed interest in having some shutters that "look like wood", so I would like to try that someday. The process should be similar, substituting stain and a top coat for the paint.