It should be very simple to host Ubuntu Server in VMware Fusion on your computer, you will need to make sure that the Network type setup for the virtual machine is set to attach to your current network rather than creating a new internal network and you will need to set your router to forward the incoming web traffic to the virtual machine. You will also have to consider how to reinforce the server with a firewall and backup utilities since it will be a production webserver.

There are good reason that we chose this platform for our ventures, I am glad that you are seeing some of the benefits now.

Now that you understand the administration, I will point to the commend from Masen, if this is a business or production server that needs high availability I also recommend for you to checkout hosted services so that you do not have to leave your home computer on 24/7 and have to deal with potential attacks across your internet connection.