mAh stands for mili-Amp*hours. Current multiplied by time. Upping the mAh of a battery will not affect your gun at all other than how long you can shoot. With higher voltages though you might want to upgrade to lower resistance wiring and a mosfet (which lowers the voltage at the trigger contacts so they don't burn and stop conducting electricity), but with 9.6v or lower you'll be fine. Even with 11.1v the gun will shoot fine for a while, then stop shooting when the trigger contacts get too burnt.
I have a 7.4v 5000mAh 20C constant/30C burst Lipo that I paid $20 for, and I go 2-3 solid days (~12-15hrs) of airsofting between charges and I'm sure I could go longer. Also with Lipos, the number with the "C" after it is the discharge rate. You will want to be careful with a Lipo that you don't let the voltage get too low because you can damage the battery and possibly yourself (when it bursts into flames). It's not like a NiCd where you discharge it and store it with no charge.
And those batteries that come with new guns are always garbage. Search eBay or Hobbyking.com or a similar store when buying a new one. Airsoft specific stores overprice their Lipos like crazy. Lipos are the way to go. You will have to buy a Lipo specific charger, but the benefits outway the $30 or so you'll spend on a charger.