What is the Proper Voltage to supply an enough Current to the Arduino
The Technical Specs say that 2.7-5.5V DC is ok so you should be good at 3.7V DC.

Remember though:  Power consumption = Current  x  Voltage

So check that your power supply has enough current available. The current amount used will depend on how many pins you are using. The maximum each digital pin may use is 40mA. 1A (1000mA) will be plenty but mAh (milliampere hours) sounds like a battery specification.

Also, a word from the wise is that some cheap power supplies can be bad (little spikes and dips). If you are having trouble with strange issues it can be a good idea to check the power is ok.