I like the idea of building this gaming rig in the Node 304: http://www.newegg.com/Product/Product.aspx?Item=N82E16811352027
I was thinking about getting this Radeon HD 7850 to put in it: http://www.newegg.com/Product/Product.aspx?Item=N82E16814150642
Would that fit and what kind of PSU would I get?
You can fit the XFX 7850 in the Node 304, but probably the cables from the power supply are going to interfere with the GPU in some way. So buy a quality PSU from Corsair, Seasonic, Antec, XFX or Pc Power & Cooling, which length is under 6.3 inches to prevent a clearance problem.
If you can post all the hardware specifications of your build we could suggest you a good power supply. But i'm sure you won't need more than 400 to 500 watts, so the Corsair CX500 or Seasonic s12II from 430 watts to 520 watts are going to be the best options for you.