Setting up a server for the house.

So I would like to set up a server for the house, the three things I would like to do with this is for it to run plex media server so I can stream the videos from this to my TV, backup two Windows machines to and host a game called minetest for me and my sister to play off of. I am looking at some guides on how to set this up but I was wondering if this will fit the needs of the task...

Will this hardware work or is it to old? What would you recommend?

Intel Core 2 Duo processor2.80GHz


4GB DDR2 SDRAM system memory (expandable to 8GB)

1TB SATA hard drive

Integrated Intel GMA 3100 Graphic

Genuine Microsoft Windows 7 Professional 32-Bit Edition

Which operating system?
Since I doubt I could get Windows server for free legally, could all three task be possible through just the Windows OS? I am comfterable in Linux enough I would imagine to setup these services, so if you all think it would be better to run a full server OS then would you recommend Ubuntu 12.04.3 server or centOS 6.5 for the given task?Any advice would be appreciated as this is my first attempt to set something like this up, I figured though this would be nice to have so I don't have to leave my notebook open and on just so people can use plex and or once I get the minetest server set and my younger sister wants to go in and play on her computer I don't have to leave my notebook on.