I would look at more HD's and set them in RAID or something if this information is important to you.
Also, 1TB will fill up fast if you plan on using it for movies and such.
Why do you want to host a website on your own PC. Unless you really good with Linux/PHP/Apache, etc, all you're doing is leaving it open to the outside world to hack and access your whole PC. $3 a month for hostgator will get your hosting 10x what your box could provide.
What kind of OS are you planning on running?
If you just want streaming, video, pics, and want to avoid the web server, you could look at a NAS box that is streamlined just for that purpose, supports, raid, runs a lightweight os, etc.
For OS, depends on if you plan on running a web server for it, then probably a full linux. If you dump the web server, then I got for a NAS only linux based OS like FreeNas or something. Very small, lightweight OS that is made for sharing of files and that's it. I would at least go 2 drives to get some protection in case of failure though. I just 2 TB of stuff for not practicing what I preach. lol.
I think I want to run a web server on it to access my files from the web from a remote location using owncloud or something like that. So you recommend linux for a file server and web server? What flavor would you recommend or does it really matter.