4Ga wire should be plenty for your application.
If you're concerned - run (2) lengths of 4Ga - its cheaper than 0.
A battery only extends the playing time of your system with the vehicle off.
Your car runs off alternator power - and it is recommended you upgrade the alternator to a High capacity one to properly supply voltage to your amplifier.
A capacitor is a cheap bandaid that will prolong the life of your stock alternator - but eventually - the alternator will die from the lage demands placed on it.
Put the battery and cap money toward a High Output alternator.
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