Sorry for the length, but you asked.
I had the AEM V1 for years. If your car is a daily driver, some people have stayed away from this style of CAI due to the possibility of getting water into your intake. That's not good. Some people have developed covers for their filter to keep water out. There is also a bypass that can be purchased that will keep water from come into the intake.
It will give you a real nice sound and I really liked mine. As for HP gains, you may get a couple, but you won't really be able to tell. If you want the most HP for the money with an intake, many people swear by the Comptech one and there are a couple more that have shown to give some HP, but again, you won't get much.
As for gears. I have the 4.77's and you WILL feel a difference with those. The 4.56's are really nice as well. I would venture to guess that more sets of 4.56's are sold than the 4.77's due to the fact that you will be driving around at a higher RPM with the 4.77's. If you would like to see what it is like to have 4.77's and be at cruising speed, drive in 5th gear down the highway. That is about the RPM's you cruise at. I have not noticed a decrease in MPG, but then mine is just for fun so I don't really care about MPG when I am in the S. I have taken it on four long drives (over 500 miles) and have gotten the same MPG I had gotten on the same drives the year before. The up side is that you have a much quicker car throughthe gears, the down side is that you have to shift at a lower speed due to the fact that you go through the RPM range quicker.
This will give you an idea of what miles per hour you will be going at the top of the RPM's. You can change the year of your S and the final gear ratio.
Turn Zero Technical Resources :: Gear Calculator