I use a standard Samsonite F'lite for my Bike Friday. BF wanted $250+ for their version. I bought the Samsonite in Ebay for $100. I also spent $10 for some felt fabric to wrap the parts while in the case...
I don't recommend building a case/box. An old suitcase will be fine.
My Samsonite gets searched about 1 every 5 trips... A homemade case/box will virtually guarantee a TSA search every time(assuming you're in the US).