We do not offer size or recommendations for complete systems. We don't deal with hardware on the front end. When you place requirements of "200mbps internet connection which will also serve up to 4 more pcs", you need a professional to assist you, like a salesperson!
I do love this requirement though:
"able to record up to 4 different channels at once and have a remote control to control it"
YOu are funnny! I can tell you already you need 4 TV tuners! NO CONSUMER MotherBoard will suffice! Good luck with that! YOu are looking at a $14,000 PC! NO kidding!
BTW, Netflix doesn't run on Linux, it requires SILVERLIGHT! You have a lot of homework!!!!!