Summary

I got nice and cheap 7" LCD on AliExpress for some $19. Its controller supports 3 AV inputs, one VGA and one HDMI. It's universal and ideal for Raspberry Pi or install jobs.

I designed and 3D printed a case and a stand. The ports are supposed to be easily accessible, so that's why they are on top and quite visible. I had to print the case in parts to prevent warping. See instructions for detailed how-to.

Instructions

The entire thing is quite big with 17 x 13 cm footprint and it was kind of problematic to print it on my Prusa i3 due to thermal warping. I had to use PLA, because with ABS it warped every time.

This thing should in theory print in just two parts and I originally designed it that way. But I was unable to actually print it. After several tries I redesigned the case to be modular. See the colored x-ray view:

bottom (red) is the baseplate. It's big, but completely flat.
middle (yellow) are four support columns. They look similar, but are not exchangeable. Use the hex holes and common sense as a guide. These columns should be superglued to baseplate. In theory, you should be able to print the piece as one, but I was unable to.
side_* (blue) are sides, which you will put in grooves in the support columns. You can permanently glue them with superglue or hot glue as well, if you wish.
- Two of them (side_short and side_long) are plain solid.
- side_buttons has five holes with hexagonal cutouts for nuts of common bushbutton switches you can use for menu buttons (power, menu, up, down, source). They aren't connected in the pictures, as I'm missing the PCB connector as of now. The hexagonal motif is repeated in the back vent holes.
- side_connector has holes for power, HDMI, VGA and AV connector. It fits the common PCB00099 controller I'm using. The v2 versions contains mounts to screw the PCB.
top (green) is the LCD frame. The LCD itself is contained within the frame, in the internal cutout. The cutout is asymmetric for the LCD I'm using and you would probably have to modify it a bit.
legs (not pictured on overview) can be inserted to vent holes in back (bottom) part to hold the screen in two possible angles.

Entire case is held together with four M3x20 screws and captive nuts. Try to find black ones, not to stand out from the black face.

Tips:

Before you superglue the middle parts, triple check that you are gluing the right part to right place. I didn't and had to print most of the parts again.
Also check if they aren't upside down, otherwise you would not be able to put the M3 nuts in place.
Cover the aluminium back of LCD with some non-conductive cover to prevent shorts (I used blue electrician's tape, as seen on one of pictures. You can use black one to hide the edges from view, but I didn't had one handy.

AliExpress links:

7" LCD enclosure