Who has the quickest and cheapest internet serice? I just got a computer?

It will depend on your service area and which regional Bell company serves you. The most inexpensive offer for high speed can be free: many cities are partnering with wireless companies to provide Internet access. I guess you can check with your City government to determine if anything is being planned or already in place. DSL from your local phone company is usually the cheapest offering and provides a good balance between speed and cost (up to 1.5mbps downloads for about $20-25/month). Cable usually offers the fastest downloads (up to 3mbps) but is usually the most expensive at $40-50/month. They do offer some introductory pricing specials.