Graphics cards are just one of a few components absolutely necessary for your computer to run normally. Some computers especially store bought ones usually have motherboards on-board video cards meaning their integrated into the motherboard. Should your video card you purchase ever fail this would mean you always got something to keep you chugging along. While you might think buying a card will cost you an army and a leg fortunately they come in all flavors meaning cheap and expensive.
ATI / AMD = Cheaper (More bang for your buck)
Price range $50~$1000+
Nvidia = More expensive (Extremely power graphics processing power.)
Price range: $50-$2000+
Now to elaborate on a few things ATI & AMD are one in the same. AMD purchased ATI in 2006 for 4.3 billion dollars. Likewise while Nvidia & Intel are separate their products tend to go hand in hand though their is nothing wrong with having an AMD processor paired with a Nvidia graphics card, or vice versa nothing is wrong with having an Intel processor paired with a AMD / ATI Radeon graphics card. Their are benefits however to having them paired which will be discussed in their appropriate sections for each respective brand.