There is no such thing as too big a wire... The better quality wire will cost more but will be smaller due to the higher quality wire. It will also have more strands in it which will make it easier to move around.
IASCA has a chart for how many watts you are running and how long the wire is. But realistically bigger the better.
Bigger Alternator is NOT required unless you have lots of speakers. Your battery needs to be good quality but nothing special and only one. The wires makes the difference. The second battery should only be added if you are going to play your music for extended periods of time with the engine off.
Thing is even if you have 1800 watts you are not going to use them at 1800 watts all the time. I had a 500 watt rated system with cheater amps. Which means it was over 2000 watts actual. I used 1/0 wire, factory alternator and factory battery. I ran my wires directly to the battery and it sounded pretty damned good. Lights didn't flicker or anything. The 1800 watt is max and you won't be maxed out for long periods of time so you should be fine. You can always upgrade the battery later and if the alternator doesn't keep it charged get a bigger one. A dual alternator is a waste of money. Just makes one more item that can break down.
Rodney