Alternator or Battery?

Since I installed my stereo (only a CD deck) and my indiglo's in my '95 LX, my stereo cuts out (and comes back on) and my lights dim whenever I push on the brakes. I'm pretty sure this is an alternator overload issue, but I just wanted to get some input form other people. I am thinking about changing out both, but want to know if it's dangerous to other components in my car to get a high output alternator and a higher amped battery? Any help is greatly appreciated. Thanks...

does you battery warning light ever come on when your driving? can you use one without the other no prob? could also be a bad ground....clean tose up first before you spend money on something you may not need