Ohm's law, yes. If your going to use a mechanical personal vaporizer (PV) get an ohm meter to check that your resistance is what you assume it should be before vaping with it. Thinner wire=higher resistance(higher ohms) thicker wire=lower resistance(lower ohms). Nichrome (not nickel) is what the first e-cigs used for their coils and because it was considered safe it was kept in usage. Kanthal came along also because is was considered safe. The reason why they are both used is because they have different electrical resistances, nichrome resistance is lower and kanthal is higher and people have their own preferences. As you are just starting to rebuild it might be safe to start with thinner wires that give higher resistances (1-1.5ohms) and are used in setups that don't require a lot of power to get a satisfying mouth to lung vape (10-20 watts). 28-30 gauge is a good place to start. I for example never needed to go lower than 28gauge. This is a good 28G kanthal here
SKU 2221000. You also have coiling calculators like this one that can do pretty much all the math for you. http://www.steam-engine.org/coil.asp
Buy batteries according to what power requirements you have (10Amp continuous discharge batteries minimum) and stay with the high end manufacturers Sony, Samsung and LG because they are making most of the batteries on the market and the cells they keep for selling will be the best always. Same for chargers, Nitecore or Xtar.
For wicking, cotton is pretty much the standard. Make sure you buy organic cotton, non-bleached or processed with any other chemicals. Ko gen do, Muji are good sources ( Japanese organic cotton) but you can also find 'selected' cotton that is intended specifically for vaping like Wick āNā Vape Cotton Bacon V2 which can be not as easy to find or more expensive but you are sure it's good cotton.
Any questions, fire away :)
Edited on 8/17/2016 at 5:16 PM. Reason: