You are correct when you said you need to let the battery run down as low as possible before re-charging... it's not as important as it used to be, but it's still good practice.
Also, if your notebook will allow you to, once the Gateway Laptop Battery is fully charged and you know you're going to be using it plugged into an outlet, remove the battery all together and let it run on AC power. (Some notebooks don't operate without the battery in place -- you'll have to try it to find out.) Put the battery back in when it's unplugged and you're going ''on the road''.
As far as the other suggestions? They are RIGHT ON with their information. Upsize...