I have been trying to research this all week with the blizzard leaving me stuck at home with not much better to do. I understand that the ego-k is a 510 battery. I do not know what options I have otherwise, single coil, double coil, 1.5, 1.6, 2.0, etc.. I don't even know what that means.
I'm on a roll, so someone better correct me if I'm mistaken!
Most ego style batteries are 510 threaded, as are most APVs these days. The Ego-K just appears to be a big capacity ego battery (1100mah) with fancy designs. K stands for King (as in big size) by the look of it.
What carto resistance you should use depends a lot on what Volts your battery is putting out. 3.3, 3.7 or VV depending on what battery you choose. If you get VV like the Ego Twist or Vision Spinner, you can use a wider range of resistance.
Double coil seems to be a way to get around that limitation on non VV devices to produce better results from a 3 ohm coil by using 2 of them to give effectively half that resistance. Will burn out quicker and use more battery life though.