I have a pretty big case because I wanted space for a lot of hard drives. It's a lot of consumer-grade equipment from years ago.
I actually appreciate all the advice, I've got a lot more information to proceed with now. I'll probably wait for a sale and see what card I really want to get, because I could also use the machine for local game streaming in addition to the transcoding, so I might wait for a sale and get a 750.
Right now the current block is that I need to do some BIOS hacks to enable RE-BAR (which has been available since PCIe 2.0) so that the Arc card works properly, but there's a nice little guide I found that's been proven to work all the way back to Broadwell and Sandy Bridge processors.
Thanks again for the advice! I love tech, it's such a world of possibilities.