If you do that, you want to use glass cleaner on the outside of it.
Exterior Flat latex black paint,and economy brush. No thinning. Should take about 4 coats...well 3, but the 4th to block out any light you missed.
Some people do just the back, some people do 3 sides.
Edit: Make sure you get exterior. It hold up better to water, and you can even paint regular wood with it to water proof it.