Your cabinet is a Williams cabinet. It appears to have been a Robotron in it's past life. (It has a smaller chance of being: Bubbles, Sinistar, Joust, Moon Patrol). It definitely wasn't a Defender. I think it's a robotron due to the extra amount of panels on the side that stick out over the cross piece, but it's dark and I can't tell for sure.
In any case, an isolation transformer is easy to connect. One pair of wires should be labeled "Primary" (usually the two on the bottom) and one pair should be labeled "Secondary" (usually the pair on the top). Just connect the primary to the neutral and hot AC wire, and then the secondary to the monitor... It's that simple. (Test with a digital multi meter set at 200 Volts AC to ensure you have them connected correctly)..
Yes, you SHOULD use a AC line filter to prevent interference from making it into the game (both into the monitor and into game boards/etc..) Computer power supplies have them built in, but games need the separate box. Wire it up just like Bob Roberts diagram.
You can steal AC line filters out of the backs of many dead consumer devices like VCRs, old AT/ATX computer supplies (they're often attached directly on the receptical end of the power cord in the power supply--look for a black receptical and a couple, typically blue colored, round flat capacitors.... just use the whole thing and make your game have a detachable cord then!