Chris - your idea should work fine!
When you signed up for Logmein you will have set up a username, password, and a long access code (forget exactly what its called).
Logmein probably installed itself on your host computer and there should be an icon in your system tray (next to the clock on the taskbar).
On your netbook, go to the Logmein site and log in with the username and password - I think at that point it will ask you for the access code. Once you've typed that in, you should be shown a list of what PCs are available to you, which should be just your host PC. Click on that and you should be in business.
Note that screen resolutions may be a problem as your home PC will probably have more pixels than your netbook. Both the screens that I work with are the same 22" size, so I don't have that problem.
HTH
Rod