FC,
This is all good information. However I do not agree that you should use Cygwin or a shell account to start with. I think you should jump in and install Linux. It seems like you only have the one laptop, so you have two options:
a)dual-boot windows and linux
b)buy an older, cheap computer from
www.ebay.com or
www.craigslist.org . For $100-$200 you can find a computer that will run Linux just fine.
If you do option a make sure you have your Windows installation disks in case things go wrong. Defragment your harddrive, then scan the harddrive for errors. Once you've done that just boot your computer with either a Red Hat or Mandrake CD and it will guide you through installation.
Here are good resources for you:
www.tldp.org (The Linux Documentation Project; see HOWTOs)
http://www.icon.co.za/~psheer/book/index.html.gz (A book/tutorial for newbies. Learn it!)
The best place to ask questions are on USENET. comp.os.linux.hardware, comp.os.linux.mandrake, comp.os.linux.setup, etc.
The best place to start searching for answers is the USENET archive.
www.google.com/groups. Search for linux + your hardware + your problem.
Another good place to ask questions is IRC, particularly #linuxhelp on the Undernet network.
Here is the guide to asking good questions about Linux. Read this and take it seriously.
www.catb.org/~esr/faqs/smart-questions.html
Ok, that's a start. If you do with a shell account/cygwin you will learn. In some ways a shell account is best: no graphics, only command line. But will you stick with that? It may be better to jump in with both feet.