having just returned to racing after 6 years myself i completely understand its a bit confusing to start with but its so much easier now.
just like brushed motors lower T(turn) rating means faster motor
esc i think for racing sensored is the only way to go but someone more experienced can answer that.
the batteries are fairly simple actually. the mAh rating s the same as only nimh 2S is 7.4V and the C rating is the current that can be drawn from the pack.
So a 1200mAh 10C battery is good for 12A (10 x 1200mA/1000) and the same size 12C battery would be good for 14.4A (12 x 1200mA/1000)
or in your example 60*6000/1000=360A
i have found that the new lipos and brushless systems are so efficient that i only need 2 sets of batteries to do a nights racing (1 in the car 1 on charge)
no doubt there will be more indepth replys so i can learn some more