I finally got all of the parts for the PC and put it together. I decided to do things a little different than just installing Ubuntu. I ended up laying down ESXi 5.1 and creating an Ubuntu 12.10 64bit VM. The reason for this is I may want to have an additional Windows XP machine for some other work that I need to do.
I got the VM all set up and am using VSphere Client on my W7 gaming PC to access the console. I then used Samba to create a file share between the two (while using a Linksys Gig desktop switch). The end result is a setup that lets me download, record, rip videos on my W7 machine and transfer the files to my Ubuntu machine to do the transcoding.
I currently have the Ubuntu VM setup with 6 cores and 2 GB of memory with 60GB of disk space from the SSD. Below are a few pictures of the build and the VSphere client display with the Handbrake menu side-by-side.
Let me know if anyone has any questions or wants to see anything else!!