Juggler, using wood probably the fastest,cheapest and best wood for the project would be 3/4" plywood.
To cut down on expenses if you can get your hands on a few good pallets you can use the white Oak 2x4s or 4x4s at the bottom, middle and top of the gun case for strength, notching the middl oak 2X4 out to hold your gun's forearms and a notched piece of pallet board on top of the bottom 2X4 oak board to hold the stocks.
If the white oak is in good shape it will provide a good solid connection for the side boards using long lag bolts or long deck screws.
You could even bolt through the white oak bottom and through a closet floor if you should decided too.. You would have to glue the oak boards together to get the dimension you are looking for but that's no biggie.
The back also could be made out of glued together oak pallet boards if they are in good shape, especially so if you or a friend has a 12" planer or bigger, any deep flaws can be plugged with a wood filler and sanded down.
Just thinking about saving you some money by going with the pallet wood. I save good pallets for their wood and for blocking.
Other ideas coming, might be able to use a few ideas to come up with one you like.