I need to fit an RFID reader and Raspberry Pi, e.g.
Into a case something like this:
What are the options and possible gotchas here?
I have the linked housing and your setup will not fit in there, but I guess you're asking for housings in general and not the particular one. Next, I think you want to know what the impact of the additional plastic is on the wireless signal.
For the housing, you could design a 3D model and then have it printed. That way it will fit exactly to what you have built.
In my company we're using RFID readers as well and they are behind a thin plastic (0.5mm maybe) and behind a backlight (2.0mm maybe) so 2.5mm in total. The RFID reader still works, but as a consequence, the RFID tag has to be held very close in fron t of the reader (~ 10mm max.) Make sure you don't have additional gap between the reader and the plastic inside the housing.
Modmypi makes a case which accepts spacer plates that raise the height of the case. You would need to mount the RFID reader to the cover (hot glue and/or some standoffs would work) but it should fit given the right number of spacer plates. One additional add on for this case is a cover for the SD card which is tamperproof.
Another option would be to create your own case, out of acrylic, wood, aluminum or as @goldilocks one of the mods is fond of, food storage containers from the dollar store. These obviously would require a little creativity, hardware and tools. They do however allow for a lot of creativity in the design.
There are also plenty of plastic and aluminum general purpose project enclosures, such as this one from adafruit, that would allow minimal tools to cut openings for the cables.
The only gotchas would be the range of the RFID reader and the extra distance between reader and card introduced by the case - this should be minimal. Material choice could also, present a problem if using a metal enclosure. Though an acrylic or plastic cover would solve this. You don't mention what model Pi you plan to use, but the Pi3 can run a little hot and in a tight enclosure it may become an issue - heat sinks/fan should take care of this should it become a problem.