800w rms system... so how do you know you need a new alt? Was it tested? an Optima would have been nice but a highish price, I think you are fine with a decent sized battery as long as the alt is good.

If you haven't noticed even in cars without stereos bad batteries tend to use up the alternator and bad alternators tend to take batteries with them (you often have to buy these around the same time in other words)

70 amps alt may be fine but if there is a factory upgrade available that might be a good idea, also an OVERDRIVE pulley on the alt will have it making more current at idle. If not then welcome to the exotic alternator world (be prepared for possible drama)

4 gauge wire or bigger is a very good idea, 'big 3' a good idea,