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There are mainly 2 kinds of swimming pool brushes that you need to know about.
The first kind of brush is the nylon brush. You can find this in a variety of widths, from 10" up to 20" for home pools use. This kind of brush is perfect for weekly pool maintenance. Remember to brush the entire pool, including the steps.
The 2nd kind of pool brush is the steel brush. This kind is perfect for those nasty stains or if you have pool algae. You'll want to scrub pretty well to loosen up all the algae spores that adhere to the surface.
This should not be used on vinyl liners or fiberglass. A steel brush can rip vinyl and may scratch the gel coat of your fiberglass pool.