The resistance of an ammeter  should be LOW because in a circuit ammeter is connected in series. so if resistance is high current didn't find a way to flow so the current won't flow to the ammeter. 
The resistance of an ammeter should be as low as possible. It should be low because an ammeter is connected in series and if the resistance is not low, the overall resistance of the circuit will be changed and the current measured will be different from what it should actually show. So, in order to minimise the error in current measurement, the resistance of ammeter should be very low.