Matrox is the name of a Canadian company that makes excellent video cards. They are a bit conservative and thus tend not to be "at the bleeding edge" speed wise, but they make very high quality, fast cards. Any search on the WEB should give you some sites that carry their cards or go to www.matrox.com for info and their online store ($100 to $200 range).
Video cards are easy to change(just unplug old one and plug in the new one). Cost effective? For pure internet use, probably not. If you use MS Office programs or similiar, it will speed things up if your existing card is not a high end one. Also remember that if you have and older system (ISA or PCI video) you will not be able to use a fast Matrox Mellennium G400 (AGP style video card).
If unsure ask Gateway to tell you what type of video cards your system will accept.