You don't need a whole lot to make a wooden enclosure. Just need to make sure the parts that would normally be getting ground from the chassis have wires to ground. Or you can line the inside of the case under the motherboard with a thick aluminum foil to act as a large ground plane.
Another option is to cut the motherboard tray and PCI slots out of a cheap case and build a wooden case around it.
Computers are less susceptible to EMI noise then they used to, but you may also consider sandwiching some type of metal between or behind your wood panels for shielding.