(This only covers the AC wiring inside a cab. Monitors are a whole new can of worms.)
What you have to remember about DIY wiring is basically 2 things:
(a) INSULATE. Try to cover all your connections. And use heat shrink or tape that is rated for 600 volts. (Or at least 300 if you are in the 120 volt region of our world.)
Pay attention to your wiring insulation too. Make sure it is rated at least 300 volts too.
Leaving bare places create likely touch points. You dont want exposed wiring if your kids, showing off your cab to friends, decide to open the box and look inside.
I would guess that the danger is a lot higher of getting shocked than fire on DIY jobs.
Exposed wiring can also lead to fires by getting together, shorting out and causing sparks, which leads into my next thing.
(2) MAKE GOOD CONNECTIONS. A loose connection will generate heat. The heat makes the conductors expand, when the power is turned off and the connection cools, the conductors contract. This moving weakens the connection even more and the connection gets more loose and will eventually lead to sparks. We all know sparks and wood are not good together, unless you are trying to start a fire. Not only sparks, but the heat from a loose connection can get hot enough to melt the insulation on the wire, which points back to (a). This heat, if covered in lint or touching the wood cabinet, can be a good source of fire.
If you use crimp type terminals, make sure they are the insulated type, and make sure you know how to properly crimp them. Make sure the socket fits the blade, it dont need to be loose.
On high voltage connections, if I do use crimp terminals (which I rarely do, I prefer soldering), then I cover the crimp with heat shrink tubing after connecting it.
If you solder the connections, which is probably the best way to go IMHO, make sure you get a good clean, shiny solder joint and cover it with heat shrink or good tape.
And a good rule of thumb is to watch your job for a few days after. Use your arcade for a good while, then look around at your connections, do they still look good? Check for insulation at the connection turning colors. Also unplug it from the wall and immediately feel your connections. Do they feel warm? Shake the wiring a bit, make sure your connections are still tight.
If you make a bad connection it should show up pretty soon, but I check out my cab wiring every couple of months, just to make sure.
Also, a good connection includes using properly sized wire. If a wire size is too small for the load it is carrying, it will generate heat, and can get extremely hot. It's always a good idea to use a proper fuse in line with the AC supply. If too much current is being drawn, the fuse blows and turns off the power, which saves the wiring from over heating.
Remember, your cabinet, your house, and all the neat things you accumulated over the years can be replaced, but the lives of yourself and your family, cannot be.
When you are wiring, dont think of the insurance company, think of this.
PS, it's also not a bad idea to have a working smoke alarm in the same room as the cab, just in case.