A "monochrome" screen refers to any display which only displays one colour, based on the type of phosphor used. The type you are after is more specifically called a "green screen" monitor. Unfortunately an internet search for this term is going to produce a lot of stuff about movie green-screens - perhaps searching for "green screen CRT" will be more helpful.
As to what type you should get - that depends on what you plan to do with it. What are you going to hook it up to? Do you want a monitor you might be able to use on a modern PC? On an old PC? A more historic 8 bit computer? A mainframe?
Historically, you're going to come across two types of green-screen monitors. First, the basic monitor designed to receive a video input signal from a computer - just like the monitors we all know today, although the input connection is going to be quite different. Most common on IBM-style PCs was the 9 pin D-connector (DE-9) although you might also find monitors that use composite video or S-Video ports, or even something proprietary to the system they came with.
The second type is part of a "Dumb Terminal" or just "Terminal". This is a monitor/keyboard combination that is designed to connect to a computer via a serial port, such as an RS-232 connector. These provide all the display hardware and character set necessary to display an image, typically 80x24 or 80x25 text. They were used for connecting to mainframes and early personal computers which didn't provide their own display capabilities. Their advantage was the computer didn't need to waste memory storing the contents of the screen, or incorporating expensive video display chips. They could also be connected over a distance, even via a modem. The computer simply sends text output to the terminal and leaves it up to the terminal to handle the display. Formatting is done via sending control codes, generally ASCII 0-31.
Common terminals include the VT-100 and Zenith Z-19, but there were many manufacturers.