aircrafking you are correct about the ma, the higher the ma the longer flight you will get, as a rule of thumb, now the C rating is a discharge rating. Lipos have to be kept within their calculated C rating of discharge or they will get hot and puff up or even fail and possibly catch on fire. The higher the C rating the higher the amp draw it can handle
Now the only thing you have to watch with increasing your ma is size and weight, because of course as you go up so do they.
Yes just like nimh or nicd the higher the V the more performance from the motor, but you have to know what V your motor can handle
I would suggest you look into a watt meter, this is a very handy tool, you hook it between your ESC and batt to tell you what amps your pulling and how many watts your producing. Take it from someone that has lost lipo's because of not having one, it's worth the 50.00. It can save hundreds in damaged lipo's due to over amping them in flight
I hope this helped