I am sure that is a fine case, Thermaltake makes nice stuff. There are many ways to go about browsing your content, ( as I am sure you are aware of ) either locally, a NAS device, or on another computer. To be honest, I would only use a small enough SSD ( 40-80 gb is plenty for most OS ) hard drive for the main operating system, and then have content stored on another device. ( windows share )
This would free up room inside the case for the Mini DSP boards, and room on the back panel for your XLR or RCA connectors. I haven't built my own computer yet, but have installed various operating systems on barebones kits. The amount of research is similar to choosing and building a subwoofer, either from a kit or a DIY design. The computer I am typing this up on is dual boot with Ubuntu and Win7.
An ITX based system should be plenty fast for HD video, although that would depend on the software suite you are running, processor, video card. ( HDCP compliant ) I have a couple year old Zotac Intel Atom/Nvidia ION nettop ( 8 inches square by about 2 inches thick ) that runs Ubuntu 10.04 and XBMC. It plays back 720p BR rips from external USB drives very nice with low CPU and GPU usage. System draws about 25 watts full tilt. I have audio from both the HDMI connector as well as the optical out at the same time. Fits my needs perfectly.
If a HTPC is what you are interested in that will fit your needs, I would talk to a reputable computer shop that also dabbles in HTPC's, and solicit their opinion. Also check out the HTPC section of the AVS forum. Installing the MiniDSP in the same chassis should be trivial once everything else is addressed.
"What the heck was that crashing noise?" Me: "oh, just tossed the shampoo bottles off the shelf on the opposite side of the house. "