Ok. Now I think I understand how the power system should work. Here's a drawing (lines with arrows on them indicates how power flows).
So the size and capacity of the battery is dictated by the motors. And in turn the thrust that the motors can supply (which varies with the amount of power it eats) needs to be defined by the total weight of the quadcopter, which in turn is defined by the weight of the components, which vary with e.g. capacity of battery.
To stop this endeless loop I looked at an Emax MT-2213 motor.
According to this it can supply a total thrust of 860grams. But that depends on the power supply. With an 11V power supply and a 10x4.5 propeller it generates 670grams of thrust (can be seen on the specs on Emax website). Now this is pr. motor, since I will have 4 motors it means 4 of these generates a total of 2680 grams of force. I think this should be good enough. I read somewhere that the thrust should be approximately twice the weight of the copter (because we need "thrust-space" to maneuver I guess and to keep it agile). This motor requires a 3 cell LiPo battery. Now we're getting somewhere.
Here's a 10x5 propeller - should be close enough. The number 10 is the diameter of the propeller, where the number 5 is the pitch of the propeller which I think is something to do with how much air the propeller cuts through pr. revolution.
Here's a 3 cell LiPo battery.
This one has got 1800 mAh and delivers 11.1V. For now I have no idea how long time 1800 mAh will keep me going for, but let's just assume for now that this is ok. They also come in larger sizes.
The final thing I need is an electronic speed controller (ESC) for each of the motors. According to the spec for the motor I will need a 20A one. Here's a SimonK one, which one shop recommends together with the Emax motor.
The three wires on the right goes into the motor (Ground, signal and power). The large red and black one on the left goes to the battery power and ground and finally the orange one goes to the flight computer.
Oops, need one more thing. Since I only have one battery I will need a Power Distribution Board to distribute the power from the battery to the motors and the flight computer.
And that should be it.
So now I have a shopping list version 1.0
Apart from this I have an Arduino Uno that is going to be the flight computer in the first version and I just ordered an Inertial Measurement Unit (IMU) yesterday, which is going to help with the guidance.
In the drawing at the top of this post I've connected the Arduino to the battery (or PDB), this is ok since the battery delivers 11.1V and the maximum recommended input voltage for the Arduino Uno is 12V. Phew!
So, where does this put us in terms of weight:
But I'm still missing the weight of the wires, RF-receiver and the frame. But I still have (2680-733)/2=973.5g left for frame and wires which I hope should be ok.
Update [Jan 3 2015 later]: Ok I did some calculations and I discovered that the 1800mAh battery would last me roughly 3.3 minutes. So I decided to switch it out for a 4200mAh one that should last almost 8 minutes). Problem is that it weighs 319g... Oh well still has some room left. (The weight has been adjusted above.)