Question About Power Wire And Other Stuff

a 4awg cable should be plenty, a larger cable will not give you more power only less resistance. As far as speaker cable size goes keep it short and the bigger the better, you can equate speaker and powe cable to a fire hose, the bigger the hose the more water flow, so go as big as possible but remeber to match your ground cable size to your power cable.

You will find out about the alt/amp upgrade soon enough, (the dimming lights syndrome) but an amp like that will probably do it. An alternator upgrade is the best idea overall, no caps, and wait on the battery. 

About wire sizes:  use the largest wire that your equipment and any future add-ons might require in the worst possible scenario....e.g. using the JBL at 2 ohms instead of at 4 ohms, etc.  To do that, add up the fuse values of all amps you are using and refer to  Power and Ground Cable Specs to choose the appropriate gauge.  The chart lists amperes and the gauge wire needed for transfer of power without heating the wire.

You can use Ohm's Law to figure out what a value is when you know any two of the four values:  voltage, current, resistance, power.  To find out what amperage the speaker wire might need to carry, determine what the known factors are.  Power in watts is 787 and resistance according to your hookup is 4 ohms.

So for speaker wire, use  I = SQR( P/R ) and the chart above to determine gauge needed to transfer the current to the subs.  You'll see that the amperage comes out to be 14, which is in the range of 16 gauge wire.

You will be adding an additional draw on the car by adding the JBL.  You can find it's actual current draw by again using Ohm's Law.  You know the power to be 787 watts.  And you know the car's voltage to be about 14 volts.  Use I = P/E, and find an amp draw of about 56 when the audio is at full volume...

...then, you have to allow for peaks in the power (due to the music source) which will spike the current draw up into higher territory, possibly near 100 amps in brief spurts....

...which is enough additional current draw to possibly warrant an upgrade to the alternator and engine bay wiring.  It depends on what other equipment you have, how much room (capacity)  the current alternator has now, and how you use the electrical features in the car (like the rear window defrost, e.g.).