Accurate recreation of vintage arcades is becoming increasingly difficult. CRT monitors are rare nowadays and, even if you find one, it will probably not support the 15.7Khz horizontal frequency used by many old arcades. A good alternative is a CRT TV with a SCART connector. If your system has a VGA output and you can configure it to use an horizontal frequency of 15.7Khz then you can use this adapter to connect it to the SCART input of a TV.
It is a reimplementing my VGA-TV converter (http://visenri.users.sourceforge.net/index.php?path=2_11&page=118) using a PIC16F18313. He project details page tells that this circuit automatically detects the polarity of the input VGA sync signals and configures the configurable logic cells (CLC) of the PIC dynamically to generate the SCART composite sync signal correctly and can generate image aspect ratio control signal as well. The basic circuit only requires the PIC and a pair of resistors and capacitors so the full circuit fits in a (big) DE-15 connector enclosure. Most VGA devices can provide enough power to the PIC so no external power source is required.
Interesting looking project of idea especially because I have built something similar around 1993-1999 without any micro-controler. My VGA to TV converter design is based on one TTL logic circuit, few transistors and some passive components:
I also made a variation of it that can output PAL and NTSC composite video:
This newer design was based on signal conversion circuitry followed by RGB to composite video converter chip AD722. I had to add a 555 timer chips to generate accurate enough horizontal sync pulses to the video signal – those need to be very accurately right on composite video to get a color image to the display.