When optics and electronics collide ....

Here's a few things to think about in no particular order;
The monitor must be close to face up. In a cocktail game there's not much choice, but this isn't the most preferred way to mount a CRT. The reason is that the phosphor on the inside of the CRT face will, over time, drop off and get clogged into the tube filaments and eventually cause them to short. This usually takes a while to occur, but it definitely happens and causes the death (or at least service) of a monitor faster than other orientations.
The mirror will want to be a first surface mirror to avoid double images. An uncoated surface of polished glass will kick back about 2% of the brightness of the image, so a rear surface mirror could give you a slightly offset ghost around the image.
The mirror would probably be at a 45 degree angle with the screen just below the bottom edge. This will get the image as large and close to you as possible. but will have the disadvantage of being able to look down and see the monitor. You could bury the monitor lower in the cabinet, but it will appear smaller and further away. You can also experiment with the angles of both the monitor and the mirror, but think "periscope" and keep the mirror at 45 degrees to the monitor face and angle them as a pair.
And to make your Windows screen readable, you will probably want the screen to be mirrored at all times. Usually a quick mod to the monitor (professionals only!) or the right video card / driver can make this happen.
Did I miss anything?
RandyT