Suggestions for remote access/optimization on New Plex Server

Hey Guys,

My friend in the coming 2 weeks will be moving to Austin, Texas where he plans to get Google Fiber (1000Mbps/1000Mbps) as his ISP.
I built the following PC ( ) to use as a dedicated media server and want to be able to fully control it remotely. Is Ubuntu's remote access features good enough? Will Wake-on-LAN suffice in cases the computer needs to be turned off and then on again?
The motherboard I bought has dual gigabit on-board NICs, can I take advantage of this to optimize speed?
My goal is to be able to have at least two simultaneous streams running at 1080p smoothly off the server over the internet and being able to control it with little to no interference physically. I'm open to buying anything additional as long as it's within reason. Any help/suggestions is greatly appreciated!