Want to buy a notebook. HELP

No, and with a router you can have several computers connected at the same time.

In order to use a Notebook anywhere, you need access to a wireless router, whether it be your own, the library's, the beeches. This is typically called WIFI.

Cellular providers provide laptop access everywhere with reduced bandwidth and high costs and you may pay by the megabyte of data.

Clear.com High Speed Mobile / Wireless Internet Service Provider is offering WIMAX technology in select arkets.

Answer this first.

Do you currently have an internet providor for your desktop? (assuming you have a desktop)

Rick

If so then a router would be your best bet. Follow KISS' advice. Ask if more info is needed.