Ok, there's a lot more to it than just knowing the right battery size. There are 2 types of batteries in that size. Both are Li ion based rechargeables. There are ICR batteries, which are low discharge, low amperage batteries and tend to have a higher mAh rating. Usually maxing around 4500. These are the batteries you DO NOT VAPE WITH! That's how you lose body parts and start fires.
The CORRECT battery type is IMR Safe Chemistry batteries. These are rated for high discharge (usually up to 35a pulse ratings, depending on the manufacturer). And while they can still vent if improperly used, they normally won't do so as violently as an ICR battery. There is a tremendous amount of chemical energy stored in these batteries. And when over-stressed, via shorting it out or pulling an excessive amperage load, etc., they can fail in very violent and dangerous ways.
I'm not trying to scare you away from vaping, but this knowledge is ABSOLUTELY ESSENTIAL to vape safely.
For reliable batteries, I generally suggest getting Sony, Samsung, LG, IMREN, MXJO or Efest. But only use Efest if you know you are well below the maximum amperage.
http://www.steam-engine.org/
That is an excellent resource for learning about resistance, amperage, etc.
As far as cotton, organic unbleached is what you want. Cotton Bacon isn't bad. There's also some great Japanese cottons out there. Japanese organic cotton is my personal preference.
