On the laptop, I would use Linux to host the site. Keep in mind that it's better to have a dedicated server, a used Pentium with a 2gb drive and 64mb of memory is sufficient for a test machine. My server cost me $25 at a local government surplus store. Then use the laptop to adminster and test the whole setup.
I have a linksys router, port 80 gets forwarded to my server's internal IP address. I would presume it would be the same for a wireless router.
Let's say you use zonedit.com, once you setup your account you will be given 2 dns servers to use. At godaddy.com, you'll need to update your domain's dns servers with the ones given to you at zonedit. It takes a couple of days for the dns servers to get properly updated.
Thats it, other than configuring Apache and your Linux server.