I think you could pretty much make anything work. Ive used a dual core pentium processor in the recent past to do exactly what you are doing with zero raid. Pre-transcoding was a must for this setup...
I'll tell you what I did about a year ago and you can go from there. This setup could download, stream to two Tv's at a time and still had room for more-
Hardware:
CPU- i5 6600k overclocked to 4.1 ghz
Hyper 212 evo cooler
16gb ram
8gb CF card and internal reader (for esxi OS)
2 x 120gb intel ssd raid 1 (OS disks for VMs)
4 x 4 TB WD has drives in soft raid 10 (dedicated to freenas)
Atx mobo with dual gigabit nics.
4u rackmount case
OS: ESXi
Created 5 VMs. I like putting as few services on each VM as possible so that if something does break (or I screw it up, lol) I don't have to worry about taking everything down.
Freenas VM: iSCSI and NFS services.
Ubuntu VM x2: plex (NFS for video storage)
Ubuntu VM: pre-transcoding and other automated file operations over NFS
Ubuntu VM: VPN and Usenet/torrent client
If you would like to know anything about this setup, just ask.