After measuring my monitor about 30 times, I marked the area to remove and then drilled starter holes for my jig-saw. For a workbench, I've been using my old TV stand; it works amazingly well. I can clamp the board down to the table so I don't need a second person to hold the board. The red things are bit of rubber so I don't mark the wood.
The aluminum bar is a guide bar to help me cut a straight line (I can't even saw straight). This worked really really well. The only drawback was that it didn't prevent me from tilting the saw from side to side; which ended up in a few uneven parts in the back.
Here's the finished square cut. It looks really good at this point, unfortunately it isn't very functional. It is too deep, the transition to the level of the monitor is sharp (needs beveled), and there is no place for the control buttons.
The next thing I did was routed the back 1/4" deep so the monitor would set in a little. And beveled the front of the monitor 45 degrees so you could more easily see edges from an angle. This was a lot easier than I thought it would be. My new router is a pretty fun toy... I mean tool. The upper part of this image shows the flat-routing on the back; the bottom shows the front beveled routing.