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The basic LCD display for a Midibox project is a 2×16 character LCD based on the HD44780 industrial standard from Hitachi. You can use a larger LCD, like 2×20 or 4×20, and the standard Midibox projects will just use the 2×16 characters in the top left corner.
Availability: Suitable LCDs are available at every well stocked electronic store and especially at eBay (search for 2×16 lcd or similar). Order numbers for Reichelt: LCD 162C LED (2×16 with backlight, 12.70 EUR), LCD 164A LED (4×16 with backlight, 20.90 EUR), LCD 204A LED (4×20 with backlight, 27.20 EUR).
Connectivity: The pin assignments of the LCD interface J15 unfortunately aren't straightforward because they were chosen to ease construction of the Core. So, you have to take special care for the interconnections. Pin assignments on the LCD modules also vary. Be sure you get a data sheet with the pinout for your LCD module.