Personally, I'd just pay $10/month or whatever and spin up a cheap VM on Rackspace, EC2 or similar with 256MB of RAM and a few gigs of disk storage. A simple web server really doesn't need a full on server (or desktop, even).
It's a bit different if you're expecting said site to get 100K+ views per day or is going to host some big database, but even then I'd probably run it in the cloud to save on bandwidth costs.
It's a bit different if you're expecting said site to get 100K+ views per day or is going to host some big database, but even then I'd probably run it in the cloud to save on bandwidth costs.