So what you're wanting to do is setup a personal, at-home-server, to host your website.
Look into installing Apache webserver
http://www.apache.org/
Its really quite easy and supports a ton of options and configurations.
And then just forward what ever ports you want from your router to the LAN IPaddress of your server-box. Then you could goto somewhere like no-ip.org, or godaddy.com and register for a domain name so people dont have to remember the IP that your ISP assigns you.
Hope this helps.