It depends if you need multiple voltages. If it was just 5v and a lot of amps, you'd need a laptop power supply type of brick. A brick puts the bulky transformer outside the cabinet and the fat cable can deliver the amps you need.
If you need multiple voltages, like if the monitor ran on 12v, you'd need either an internal power supply
Or a brick that delivers multiple voltages.
LINK Some old LCD monitors need one of those power supply bricks with multiple pins for multiple voltages. The hard part would be to source the panel mount connector you need, or just snip off the connector and use some other kind of 4-pin connector.
Powering the Pi is easy, you can just solder directly to the 5v and ground lines of the USB connector, or cut off a micro USB cable and connect the 5v and ground wires to your 5v power supply directly. The new raspberry Pi's are pretty power hungry, your enemy is a cheap power supply that will undervolt your Pi or give a lot of resistance and heat. Giving it fat copper/connectors that can supply a lot of amps is what you want. And nothing sucks more than the emulator slowing down with that little undervolt lightningbolt icon in the upper right in Emulation Station.