This option gives you the most control over what you can do, but there are a few things you would need to consider:
You need to have the training on the Operating System (usually Linux) the Web Service (Usually Apache) and all other services you plan to support, this could include: PhP, MySQL, Perl, CGI, XML and a potential host of others
In Addition to the basic running of the site you also need to address the services needed to keep the site safe, things like security and backup systems, access control, allowed ftp, telnet or ssh services
Static IP