ESC motor and battery matching
Most brushless ESCs will run pretty much any 3 phase brushless motor so long as it doesn't draw too much current or spin too fast. 

Your ESC is rated for operation at 6-12V, which suggests that you could use a 7.4V or 11.1V Lipo battery. Battery capacity and 'C' rate should match the expected current draw and run time. For example if the average current draw is 15A and you want to get 10 minutes then you need at least 15*(10/60) = 2.5Ah or 2500mAh. 

To avoid draining the battery completely you should add 20% to the calculated capacity (making 3000mAh in this example). If peak current draw is 30A then the 'C' rate needs to be at least 30A/3Ah = 10C.   

All brushless ESCs have a maximum commutation speed, beyond which the motor may stutter or lose sync. With a Kv of 2200rpm/V your motor will spin at ~11.1*2200 = 24400prm on 11.1V when running free. It has 14 poles, so it is electrically equivalent to a 2 pole motor spinning 7 times faster, ie. ~170000rpm. Some ESCs can handle this high rpm, but others can't (see here for examples). Your ESC's rpm limit is not specified, so you will just have to try it.         

Motor current is determined by voltage and loading. With good cooling Your motor should be able to handle ~15A continuous or 30A peak, which on 11.1V is achieved with a 5-6 inch propeller (test data here). Since your ESC is rated at 30A it should be safe so long as you don't overload the motor.