It's important to choose an amplifier with the right output power, because too much power can damage the speakers. Typical amplifier 'wattages' for desktop & small portable speakers: 10-20 Watt per channel. For home stereo & home theater: 50-100 Watt per channel. (The exact value depends on the speakers.)
Both the supply voltage and current affect the maximum output power of the amplifier board. The manufacturers publish the minimum and maximum voltages for the board. Using the board at much lower voltage than the maximum voltage will prevent the amplifier from reaching the nominal power and you lose headroom. If the power supply current is not enough, then the voltage will drop at high output currents and the power supply may even turn off.