So basically your battery is what depends on your coil. At a full charge your battery is 4.2v which would fire a 0.5 ohm coil with 8.4amps and 35.28 watts. So you need a battery that is rated over 9 amps. As you use your device the volts will go down. At 3.7v you will be firing 7.4amps and 27.38 watts. With a 1.2 ohm coil at 4.2v you are only firing at 3.5 amps and 14.7 watts. So you definatly want to make sure your battery can handle the amps.
Here is a great list of batts.
Never stop asking questions!
Here is a great ohm calculator for double checking your safety.