The idea of speedpainting is to get an idea across in the shortest amount of time but still be able to tell what it is. The focus is on the overall image not little details. The brushes you use do not matter. Depending on what you are trying to paint, texture brushes can speed up the process if used correctly. I would suggest having a look at Feng Zhu's website he has a really nice collection of tutorials that might interest you.
With speedpainting, you aim for speed. There are no shortcuts here either. Just use whatever brushes you got, and maximize your efficiency. It also helps to create some brushes yourself, if you need stuff that isn't included in your software package.