Port forwarding wont work because residental ISP plans block port 80, thus anyone using the website would have to manually type in a different port number. Fine for personal use, but not good for having anyone else connecting to your website.
It will be much easier to just get a hosting plan from an internet provider.
To host it yourself you need:
The domain
A Comercial internet connection
A static IP address(most ISPs charge extra for this even for comercial customers now)
You need to pay a DNS hosting service (without this when someone types www.yourwebsite.com their computer has no idea how to connect to your web server).
A web server
A firewall would be strongly advised
Most small businesses opt to use hosted web servers because first and foremost they are cheap, come as a packaged deal, they dont have to worry about network security or maintaining a server 24/7.