The 60-amp rating on the ESC refers to the maximum it is designed to handle, not the amount it will pull constantly. How much current flows depends on the motor and driving conditions.
In addition to their voltage and capacity in mah, batteries will describe the rate at which they can be...
It depends on the vehicle you're going to be putting it into. Standard battery mounting trays are a certain size, but you might have room for a longer one, or less room intended for a "shorty" pack. You may want a "hardcase" battery, and you'll want to make sure whichever battery you choose...
That's rated for a continuous discharge of 4.9 amps, highly unsuitable for performance RC applications. It would be good for something like a TX pack. 18650's have relatively low "C" rates compared to "pouch" style lipo batteries, even the "high-drain" ones top out around 10C.