Plex Media Server quick/long question

I'm trying to figure out if something is even possible however I'm not familiar with the vernacular.

I only have an underpowered PC and it's a laptop. It rarely is always on and when it is it's not really that much of a beast; just enough to run what I need ran. I have a large and ever growing Library and have completely cut cable. In my living room I have a Roku 2XS, appleTV and DVD player. I'm looking to rip all those DVDS and get rid of the player.

What I want to do is this (Forgive me if I don't call it quite correctly). Rip all my DVDS to a hard drive and then somehow install Plex on that drive. Then hook the drive up to the router directly and use it to house all the media. Through the Roku then run the Plex app and have easy access to all my media without all the mess of the accumulated cases.

Is this possbile. I'm not really financially able to get a dedicated PC for the server. I'd like to manage it all on one drive and maybe for good measure just remotely view the server (not sure on that either). If I could remotely view the server I could, through cloud storage I think, easily put files onto it. Or just directly connect it to the laptop after ripping.

Anyone know a way to do this?