Home Theater PC Build

[Tywin]

I'm wanting to build a home theater PC that'll be used only for storing and playing media on my TV. 

Aside from hardware suggestions, I first have a question. 

 

Every time that I have ever plugged a PC into a TV, the resolution always seemed to be off. I don't want to waste a few hundred dollars on a PC and spend time transcoding 30GB blu ray discs just for the quality to be less than perfect. 

How do people use PCs for this purpose without the quality loss? (I have a Vizio M60-D1 if that somehow helps you answer this question) 

 

 

My budget is around $350

A console shaped case is ideal. It doesn't have to be as small as a console, but flat like one would be ideal for my entertainment center.