Shizuka, you sound very sensible. A netbook like the Dell 10V is a good introduction to the world of computing. It is so small and light you will be able to take it everywhere with you, yet it is fully featured with a great screen and keyboard.
A question: how did you get online to post on this forum? I ask because you are unsure about which ISP to use, yet you must have used one to get online here.
Using a neighbor's wi fi is not a bad idea, but best to get permission first. If you live close to a McDonalds you should be able to connect to a hotspot there. Verizon is currently offering a HP netbook for $199 with a $39.99 monthly acess charge. Of course, you could always get cheap dial-up for under $5 a month but that's a worse case scenario and not very practical.
Let us all know how you get on and what you decide to do.