Wells-Gardner U5000 Model # 25K5108... Not sure about the sync and scan rate questions you asked but maybe the model info will help enough.
Here is the service manual for that monitor:
http://www.wellsgardner.com/pdf/Service/U5000.pdfThat is a 15/25kHz monitor that must be manually switched between the two, and it accepts both composite and separate sync. 90% of games in MAME run in 15kHz progressive, meaning a resolution somewhere around 320x240 progressive (240p). Not much runs in 25kHz, so you're going to want to leave it in 15kHz, and run Windows in 480i, and most of your games in 240p.
The breakout cable is the one sold by ultimarc.
It has a VGA connector one on end (for the PC), and five BNC connectors on the other end (for the monitor) right?
Physically, all you have to do is hook it up using this cable; BUT it will not display correctly until the computer is outputting a resolution that works with the monitor. If you feed the wrong scan rate into the monitor it's possible to damage it.
That monitor doesn't work with the high resolutions a PC normally puts out. Luckily, it will work great with proper arcade game resolutions. You need to set the monitor to 15kHz, and you need to output 15kHz resolutions from the PC (240p or 480i).
I'm going to be honest with you. It sounds like you want someone to tell you about a switch you can flip, and everything will just work magically. It doesn't work like that. If you don't know anything about scan rates or sync, you're not ready to get this working yet. You're going to need to put some time in and research this stuff. Who knows, maybe you'll find that you enjoy it.
Take a look at the second link in my signature, and start reading there. It's all about outputting the resolutions you need from a PC and setting up MAME for all this. It talks about using a 15kHz TV, but it will all apply exactly the same to a 15kHz monitor like yours. Just ignore the part about a VGA/RGB to component transcoder. You don't need that, as your monitor will accept VGA from the computer directly.