To properly answer the question, you need to know the capacity of your stock alternator and the amount of current that your system regularly draws. If you are regularly exceeding the capacity of your alt, the battery will be a temp fix, and eventually you will kill the alt and the battery.
Any way you look at it, the "big 3" should be the first thing you do. From there you need to look at your alt. It is the source of all the current in the car. The battery stores some of the current but the primary duty of the battery is to start the car. Once the car is running, the battery pretty much sits idle idealy. If you exceed the capacity of the alt, the working voltage of the car's electrical system begins to drop until the battery begins to contribute from its current store at around 12.5V. The drop from the alts working voltage of 13.5-14.4V to the battery's discharge voltage is what causes your lights to dim. As soon as the demand on the alternator decreases back to a level within its capacity, the voltage will go back up. At this point the battery becomes a load on the alternator, since it is no longer fully charged. If you have another spike in demand before the battery is again fully charged, the battery contributes even more of its reserve and becomes even more of a load on the alt until full recharge. Basically if you keep going in this way you can get to a point that the battery is such an additional load on the alt that it is running at max capacity constantly and any additional demand from the stereo is digging the hole deeper. My basic point here is address the alt first and then worry about batteries.