I’m also trying to make an arcade machine with an old CRT TV.
You can use the composite output (in the PI2 integrated with the sound in the the Jack connector), you will need a special cable for it, be sure it will work with the PI before purchasing.
For better image quality, I am trying to connect the PI to the CRT through the RGB connection in the SCART of the TV. For this I need a HDMI to VGA adapter and after that, a VGA to CGA downscaler to convert the 31kHz VGA signal to the 15kHz that needs the CRT TV. I have bought both in Amazon, waiting for they to arrive. When I had tried them, I will post my opinión…