battery big 3 upgrade

I have a 2008 honda civic, with factory Alternator. when im listening to music too loud the amp sometimes cuts off and my subs stop for a few seconds then comes back on and repeats. i was wondering if the big 3 upgrade would actually help with the factory Alternator, or would i need to replace...

I have a stock 206 Toyota tundra an want to b able to run a 2000rms amp...tell me the cheapest way to do this