Are you talking about web hosting, or DNS? These are two separate services.
For DNS you really should have at least two machines. They wll back up each other for redundancy. However, unless you very large, and running many domains there is almost no reason to try running your own DNS server. Almost all registrars will host the DNS for you for free.
For web hosting, you only need a single ip address. In fact, with Virtual Hosting you can host any number of sites.
Alternatively, you could pay for a web hosting service. (There are tons of these on the Internet) They can manage your DNS for you (if you like) and provide space for your website on their servers with a reliable Internet connection.