second battery will only help with prolonged listening with the car off... the alternator still needs to keep the batteries up when the car is running.

A capacitor is not really a "band aid" solution, if its matched to the system properly, it helps a great deal.

it all depends on what amp it is... saying "I have a 1000 watt amp" dosent tell us crap... as some people refer to their $15 computer speaker system as a "1000 watt system". Give us more details... if the amp is running subs or your main speakers, how you listen to your music, brand, model #, model of your car (different models have different output alternators)... tell us whatever you can, then we can try to help you.