What kind of server are you talking about here? Web server for the internet? Network Attached Storage for easy file sharing? E-mail? Proxy?
As for the OS, be warned that most "server" Linux distributions are command line only; servers don't have screens, so there's no point wasting resources on fancy graphical stuff. Web browsers, as far as I know, don't work here. You'd probably want a standard Linux OS like Mint if you're going to be using Hulu. Another note: last time I checked, NetFlix uses MS Silverlight, a proprietary plugin that has problems with Linux. To serve web stuff, you'll need a serving program (LightHTTPD is my recommendation), which should run fine on standard Linux.
I haven't used web TV much, so I might be wrong, but if you ask me you should ditch using a server OS and go graphical. You can still host a website or files or whatever, and navigating web TV will be a lot easier.