What type of gauge wire?

Nothing happens when your wire is bigger than required.  All that does is keep you from needing to upgrade if you decide to add more power to your system.

Another thing to take into perspective is that carpet does absorb some energy from your system.  So, when running wires under your carpet take into consideration the length of the run and other conditions.

So the thicker the wire, the less resistance it will have?  If you wanted to have close to nothing resistance could you use a wire with a 1in diameter?  What about the number of strands?  Which has more risistance; 1AWG with about 100 stands or 4AWG with 1024 strands? 

Does the purity of the copper wire matter significantly like the wires sell on e-bay with 100% copper?  I have two batteries hoked up in parallel and I'm using 3 6AWG wires bought from OSH since they only cost me about $10 for about 50ft.  I think I'm getting more than a .5v difference in my batteries with the car on.  Would a 2 or 1AWG help significantly?