I tried putting my media on a 2TB Time Capsule and although it worked, I wasn't happy. For one thing, the internal disk in a Time Capsule is really slow and an external disk connected to it is even slower. Even worse, the disk spins down after just a few seconds if you don't access it. That results in a long delay to start playing anything.
I ended getting a base model Mac Mini for $500 (big box stores have been blowing them out on sale for as low as $350 recently). This is more than powerful enough (actually overkill) to serve iTunes content. And it's dead simple, just enable home sharing.
I have 3200 songs, 650 movies and 600 TV shows on my server which takes up about 1.5TB. So with a 4TB external drive, I have plenty of room to grow. I have two additional drives that I rotate for backups that are done nightly with a Carbon Copy Cloner script. Very happy with this system after almost three years.
But as has been said, you don't really need a new computer for this, it could be almost anything (Mac or PC) that will run a version of iTunes that supports home sharing. I found this article helpful when I started out:
http://www.techradar.com/how-to/software/applications/how-to-set-up-an-itunes-home-server-1305683
I'm confused by that part. How are you using the video on your TV and iOS devices now if it's not in "iTunes format"?