The capacity of the battery is irrelevant - the current being drawn through the ESC by the motor is what is important. You will be fine with your 30A ESC 'cos your 600 will only draw (at max) about 20A. One end of your ESC will have just a single dual wire lead ("to motor") coming from it. That COULD be directly attached to the + and - of your motor, but I think you are better off putting a connector on it (female Deans Ultra or 3.5mm Jeti would be good) and having a matching connector on your motor leads (male Deans Ultra or Jeti) At the other end of the ESC there will be a three wire lead with a flat female Hitec/Universal plug which should plug into Channel 3, if you have a standard GWS receiver, AND a dual wire lead. This "to battery" lead will need a male Deans Ultra or Jeti connector on it, so that it can be connected to your battery (which, again, needs a matching plug on it - female Deans Ultra or Jeti).

Hope this helps, Cheers, Phil