The "brown algae" is actually diatoms. This is a common feature in a tank that is cycling. Yes, the more desirable green algae will replace the brown as your tank ages.
Phosphates and silcia are food sources for diatoms, which is why you see them in new tank setups. [A lot of silica in new substrate]. As the diatoms eat this, the bloom will diminish. Check your water source to make sure that it is not high in phosphates.