That max current is your peak number and while having a battery that can put out that much is nice, you should rarely need to max them. Having a battery than can put out 4x20 is a better average. As for ESCs, unless you plan to even lower KV motors in the near future, that seems a touch overkill, but no harm done in that.
For battery size and flight length, my average amp draw is 6x20a, 120a, and my 4s 16000mah 10c nominal battery has more than enough in it for slow cruising flights with minimal heat buildup. If you upgrade to bigger, more power hungry motors, you would eventually need to upgrade to a bigger battery. My build is designed for camera and FPV/Photography using a gopro, with a flight time of around 30 some odd minutes, wind depending.
I recommend that you figure your average weight you will be lifting and reverse figure your overall needs while leaving some weight for fighting sudden winds.