You can use a conventional monitor (old school CRT or a modern LCD/LED) if you are making a glass, lexan or plexiglass desk. Look into the Peppers Ghost effect.
I used it when I did effects for haunted houses and Halloween decorations with great effect. Read up on how it works on Wiki, and maybe check out some examples of the effect by searching it on youtube
There are a lot of how-tos online at making this work. Depending on your setup, you may need to run an app to mirror or reverse the display (hard to find these days, I recall a program called PVCMIRROR) . If using an LCD or OLED panel, you may be able to open it up, and physically flip around the panel inside to do this. I'm also sure that many Nvidia cards allow you to change settings for reflection, essentialy allowing you to reverse or mirror it's output.
Otherwise, you will need to reflect the image from your monitor off two mirrors (an extra mirror is employed to reverse the initial mirrored reflection, so it's oriented correctly)
Hope this helps. It's definitely doable, especially if your monitor is situated under a desk.