I have used wood before, and you will just want to have wire with ring terminals tying the power supply outer case to the motherboard ground and back and front panel grounds so that you dont have a floating ground.
Years ago I made my own upright and table top arcades using old computers. Back when you could get a 8088, 286 or 386 computer on the cheap or even free in the late 1990s, I would build up an upright arcade from plywood and then paint it black and install the old computer and the DOS games of a PacMan freeware clone would boot off of FreeDOS and run off the 1.44MB floppy disk containing the free game and OS. Mount the CGA, EGA, or VGA display and have plexiglass at an angle to give it the arcade feel. I altered a keyboard and wired it to the push buttons and joy stick ball on the operator panel. I did this mainly for the fun of it and sold a couple. The people buying them knew they were clones and not originals, I didnt want to get into trouble with anyone thinking they were original arcades in any way. I showed them the guts and how it was built etc, so they clearly knew it was a mix of carpentry, electronics, and computer knowledge that came together for its creation, and I wasnt charging for the software that was free on the internet, just for my time and materials. I gave up on this when I ran out of time to build these and the people who requested them stopped asking for them.
Additionally they did not have coin slots and there was just a reset push button that was tied to rebooting the computer inside and the game was set to automatically load on boot. So there was a difference than true arcades, but as far as the feel of them and sounds and all everything else was there except for the fact that they were narrower uprights with 14" and 15" CRT displays mounted at 45 degree angle leaning back in the cabinet.
I've always wanted to make a Lego Case myself, but I havent found the legos to make it yet. Even used legos have a premium to them online. And yard sales you would think there should be some for sale cheap, but i havent been fortunate yet to find some cheap.
Buying the legos to make the computer case would cost over $150 + the super glue to make the blocks permanently bonded together.
I set this idea off to the side and looked for an alternate case and ended up using a friends dead IBM 5150 that a he gave me under the agreement that I couldnt fix it or sell it, and that I had to make it look like an original IBM 5150, but with modern guts, and i could keep the computer build in the end. He just wanted pictures of before and after but had no need for the system. He just thought it was cool to have this old dinosaur of a computer that could run Windows 7 etc.
I cut and modified the inside of the IBM 5150 case to take modern parts. It was tight making it all work, and heavy modification to reroute PS2 ports, Video, Audio, USB, and NIC. Most people go the route of cutting the back of the case out and then welding a modern motherboard/card slot caddie in place. I kept with the original case and just added custom extensions to populate the card slots of the original IBM 5150 with modern ports.
The only feature that is a give away that something is customized about this computer is on the front the hard drive black panel with red LED I added a push button for soft power front panel power switch to boot the modern mATX motherboard.
One of the coolest mods in it was taking a DVD-RW drive from a Toshiba Qosmio laptop which is the type of trayless drive. I mounted this behind the face of a 5.25" floppy drive, soldered the red LED to the optical drives LED so the classic 5.25" floppy drive LED lights with DVD-RW activity. I cut the floppy disk lock to make the 5.25" disk slot always open for a disk without requiring opening and closing of the disk lock. And put a laptop IDE to desktop IDE adapter onto this so that it was functional. So you can put a DVD or CD into the 5.25" drive slot and the drive accepts the disc the same as a car stereo trayless optical drive accepts discs.
I could go on and on with all the modification but running out of time typing this. I have a youtube video on this build running Linux for an OS. While some people think its the coolest mod, I have gotten a lot of negative responses with people who are upset that I butchered a classic IBM 5150. Thing is that, it had to go through this modification and it wasnt my property until after the modification was completed. So there was no saving of this system as for the owner of it wanted its conversion. The guts though didnt go to waste. They were given to this other guy who is a collector of old computers and he used the guts to fix those. So really the only thing destroyed was the case, but the guts live on in other original cases.
I love building and modifying stuff, its like art but more enjoyable because it serves a purpose other than decoration.