help Off site media server build?

[Swedish-Chef]

Hi all,

I would like to build a low powered server for offsite use Mostly media films, TV, Music.

Off site I have 70Mbps download and 22 Mbps upload. 

Onsite I have 17Mbps download and 0.9Mbps Upload.

I would like to create a media server mostly for my use only maybe with Plex or something similar (any suggestions would be great) where I can download the content at 70Mbps and stream it to myself where ever I am.

I would like to go for something Intel based and low powered, I am not completely against re purposing old servers I just don't know what to look for.
I want this server to be able to store around 4TB but making it expandable would be good.
I would like the server to encode the video so I can watch it on my iPhone or what ever tablet I am using.
Micro ATX would be good I want it as small quiet and low powered as possible as it will be on 24/7

Can some one please help me with some ideas of what too look for or a good server build. I don't want to spend a fortune. Any budgets welcome I want it to be as cheap and as good as it can be.

Thanks hope some one has some ideas I am normally pretty good with gaming builds and desktops but when it comes to servers I have idea what to look for.