I'm not sure you even need to go as high as a Core i3 for transcoding purposes. I built my unRAID server around a G530 and it seems to handle Plex + transcoding fine. I haven't tried transcoding a full Blu Ray mkv file however because I'm not willing to blow that much storage per movie.
As far as building versus purchasing, don't be intimidated by the "NAS" operating systems. I have tried a couple of them and they really are quite easy to use. I have the most experience with unRAID, and installing that is literally a matter of copy a few files to a USB drive and booting. Installing Plex simply involves copying a single file to that same USB stick. You can always try unRAID, FreeNAS, Amahi, etc. in a virtual machine just to see what they are like.