I want to eventualy buy the cheapest laptop possible because I hate using the library computers NO PRIVACY, so what would be the best deals?

Check this out - best prices out there ! http://www.tigerdirect.com

Find one on eBay.

I personally would go with Dell's "Reconditioned", if you are on a tight budget.

Check out Dell.com You often can find a sale on a quality laptop at a very reasonable price. I just bought one with the Intel chip (to me this is the best chip). It isn't the fastest, but has a good hard drive for basis tasks including the internet. My total cost was less than $600 and includes a router for wireless connections at home and the capacity to "hop on" to the wi-fi sites of coffee shops, motels, etc. It includes a 6 hour battery (but don't get your hopes up too high-that is under the very best of conditions, etc.) but 4 seems to be more typical. (Dell Inspiration without a lot of expensive software)

Netbook -- http://en.wikipedia.org/wiki/Netbook -- Small, lightweight, long battery life, running Windows 7. I've seen them on sale for as little a $200.00 (USD). Not good for gaming, but excellent for everything else.