If I wanted to do whats laid out here: http://osxdaily.com/2010/03/22/how-...-media-center-server-and-remote-torrents-box/ would it be best to get the server edition mac mini or the normal one?
Looks like either will work. The article says "the newer the better" which means the quad core model will work best, the only difference aside from hardware being OS X Lion Server.
What is the difference between Lion server and the normal Lion? I mostly want this to stream movies from my house when Im at school or at a friends, etc. Am I able to hook up an external hard drive for the streaming also?
Am I able to stream the movies to my MBA/iPad/iPhone if Im not on my home network such as at college/friends/vacation?
Yep, sure are. I'd recommend Plex for this. I believe the iOS app is $5, but the server client to install on the Mini is free. Another popular streaming app I see advertised around here is AirVideo.
One limiting factor to streaming is going to be your ISP upload speed. Try running speedtest.net to look at your upload speed. Anything less than 1Mbps will lead to bad quality. Higher is pretty good.
Edit: Forgot that you were considering Plex already haha. You'll need to forward port 32400 on your router to the Mini to be able to access it from outside of your network.