Display Selection
There are multiple factors that go into display selection. The most important one is probably the viewing angle, since you and your players will be sitting around the display, viewing it from a large angle. Besides that, issues related to screen burn-in and image retention should be considered, since mostly static images will be displayed.
Below is a comparison between different display types, but it should be noted that there will be a lot of variance between different displays of the same type. For example, on paper, a TN display should not be great for this application due to their bad viewing angles, however, some higher quality TN displays can offer great viewing angles.
This should only function as a guideline, the best thing to do is to go to a local electronics store and take a look at the displays in person. Walk around them and view them from all angles, and see how the image changes and how different TVs perform, especially from up-close.
LCD Displays with LED backlight
LCD displays with LED backlights are by far the most common and most budget-friendly displays. They generally make a great choice for tabletop applications. There are many differences between different LCD displays, mainly determined by their underlying display technology. The most common are TN, VA and IPS. Not all manufacturers advertise which technology is used in their display, so it might be difficult to choose one based on that, but here are some important differences between the 3:
TN: TN are generally the lowest quality displays, with poorer colors, smaller viewing angles
VA: VA displays can generally be regarded as the middle class, better colors and bigger viewing angles than TN displays. Contrast tends to be the best of the 3 technologies. Brightness is better than TN, but similar to IPS.
IPS: IPS displays are in most aspects the highest quality displays. Colors and viewing angles are the best, brightness is similar to VA, but contrast is slightly worse than VA but better than TN.
OLED Displays
Organic light-emitting diode (OLED) displays can offer great contrast ratios and very wide viewing angles. However, they can suffer from screen burn-in and image retention issues on static images (such as battle maps). They also tend to be significantly more expensive than LCD displays. Brightness is typically lower than LCD displays.
QLED Displays
Quantum dot (QLED) displays tend to be brighter than OLED, similar to LCD displays, however, their contrast ratio is lower than OLD displays. Viewing angles are in-between LCD and OLED displays. Similar to OLED, QLED displays can suffer from screen burn-in and image retention issues on static images (such as battle maps).
Plasma Displays
As mentioned above, plasma displays can emit infrared noise, so should be avoided, if possible. They can have great contrast ratios and wide viewing angles. However, they can suffer from screen burn-in and image retention issues on static images (such as battle maps). They require a lot more power than modern displays, which might cause overheating issues when laying the display flat.
LCD Displays with CCFL backlight
Similar to plasma displays, LCD displays with CCFL backlight can emit infrared noise, so should be avoided, if possible. They will also consume more power than modern displays, which can cause overheating issues. In this category fall mostly older LCD displays, since LED backlights have replaced CCFL in practically all modern TVs.
The actual LCD technology is similar to LED displays, so the same considerations regarding display technology apply.
Projectors
Projectors are a completely different type of display, with their own advantages and disadvantages. To use a projector, you will have to mount it above a table, which will probably mean that you need a short-throw projector. You will also need some surface to project onto, which could just be something like a white cloth.
Projects will provide a great viewing angle (although this can be dependent on the projection surface), but can suffer greatly from ambient light which will reduce the brightness and contrast of the image. You will want as little light as possible, but a perfectly dark room would probably not be great for gaming. So a projector with high brightness would be desired.
Regarding the projector techonogy (LCD or DLP), the difference tends to be minimal. LCD can deliver higher quality images but can suffer from burn-in and image retention issues, while DLP tend to offer higher contrast ratios.
Projectors tend to emit some infrared light, but it is unlikely that this will negatively affect sensor performance, unlike some displays (like plasma displays).
One last disadvantage of projectors is that minis and hands will cast a shadow on the projection surface, something that might be a deal-breaker for some people.