There's no real need to bathe your cat, unless they get into something that would be dangerous for them to groom away (oil, etc.) or they have some other problems (fleas, ringworm, etc.). When you groom, you should always brush in the same direction as the coat, from front to back, not against the grain of the coat.
As for brushes, I likely won't be too much help, since my cats are both long haired. However, my adult daughter has a short haired cat (the cat in my avatar). My daughter likes to use a hard brush for normal grooming, along with the Furminator for occasional grooming (perhaps once every few months). I know others swear by the Zoom Groom. You will likely need to try out a few and see what works best for your cat and which she likes the best.
As for brushes, I likely won't be too much help, since my cats are both long haired. However, my adult daughter has a short haired cat (the cat in my avatar). My daughter likes to use a hard brush for normal grooming, along with the Furminator for occasional grooming (perhaps once every few months). I know others swear by the Zoom Groom. You will likely need to try out a few and see what works best for your cat and which she likes the best.