Well, I had the same problem and had to find out that this question is a rather hard one.
This blog entry introducing the official 7" RPi display explains some of the most important keywords involved (HDMI, DPI DSI, DBI).
If your display needs to be a touch screen, than the first important aspect is, that (from my research) only displays connected via the DSI-port (J4) or GPIO will not need an additional data connection for relaying the touch input. If your display is connected via HDMI, then an additional connection (usually via USB) is needed (and will have to access the USB ports from outside if you do not want to solder around - this might conflict with your casing). You should be able to get this information easily.
The next important aspect is, that displays using the GPIO ports usually need special drivers (either to be installed on a standard raspbian or delivered with a non-standard raspbian provided by the manufacturer of said display). This complicated things enormously, as those drivers might be documented badly or outdate fast - even the next update of your OS might render them useless - not to speak of difficulties using OSes that there is no driver for. You should be able to find the drivers and some customer feedback online. If you can't find the (correct) drivers or some support easily, then you will most likely have troubles using the displays once you bought them.
Furthermore, displays using the GPIO ports usually need to provide an additional GPIO breakout in order for you to be able to use some of the GPIO ports for something else. This information should be obtainable by looking at pictures of the displays (is there a GPIO "outlet" somewhere on the screens backside?).
TFT, LCD (or maybe even LED, oLED) are different technologies for displaying stuff. Although they determine the optical quality and power consumption, I personally would not worry about those too much.
More important - at least in my opinion - is the touch technology, meaning resistive or capacitive. The former should be used with a stylus and usually can't take gestures ("multi-touch"), the latter is what modern smart phones use.
And lastly, regarding compatibility with RPi3 (as opposed to RPi B+ for example), DSI and HDMI should always be fine and regarding GPIO I would go with the manufacturers information (as they are the ones, who provide the firmware/drivers). Hardwarewise, there shouldn't be a problem.
To become a little bit more specific, the only DSI screen I found, was the official 7" one. It will work without any alteration to Raspbian (I don't know about other OSes). There are quite a lot of GPIO screens of which I would use the ones by known manufacturers sold through major outlets in order to avoid being stuck with bricks (At my department, we have several displays we can't use anymore, because they are cheap knock-offs whose firmware is nowhere to be found anymore.). And regarding HDMI: As HDMI as well as the touch device (whose information are being transmitted by USB) are standardized, there should not be a problem regarding any of the major OSes.
I hope this answers most of question. If not, just clarify your question in the comments.