This thread answers your question.
If I had no woodworking experience and was making a CP to demonstrate how fun it could be and wanted to have it up and running in a weekend, I'd make a rectangular box. 
--Buy a circular saw and a drill. 
--Get a $5 2'x4' sheet of MDF. 
--They should have wood glue where you get the MDF, but if you want to screw it together, you need to drill pilot holes, or it will split.
--Make a 
saw board so that I could make straight cuts. 
--Cut a top, front, back and two sides. If the CP is going to be 2' wide, you already only need to make three cuts and the top front and back are done.
--Use a 1 1/8" 
drill bit to cut button holes, a hole for the joystick and a hole in the back for the wire to interface with the computer.
You need a jig to make any cuts with a router, straight or curved. It spins at 20,000 RPM and is impossible to hand hold and get acceptable results. 
Here's a thread on making straight cuts. 
The curved cut is not a trivial undertaking, you'll need a jig or a pattern and a pattern bit. You'll probably need to spend a lot of time sanding it too. I'm not saying don't do it, but the curve alone could take you all weekend. See 
this thread for some really nice woodworking.