Hi ark_ader, thanks for your comment. Just to clarify, are you suggesting to build the PC inside a small form-factor case which is then installed inside the cabinet? I understand how that would be beneficial if I wanted to re-purpose the PC, but how does that cut the build cost in half?
I would go with an AMD A10 78 series CPU and a ITX board with 8gb and a basic HDD, and if you have a spare SSD even better. Using the APU you will be able to play anything mame related and some AAA games too. I would get a 200W pico PSU and forget the external GPU, then have it in a SFF boxed case and slide it into the bartop. Remember you will be gaming on the bartop about a few hours a week at best, and that mini build could be used for all kinds of kewl projects.
We always go overboard on PC gear, and yet we forget about thermal dynamics, and excess costs. Like I said in my other posts, the RPI3 is taking over my intel based PCs, cutting thermals, electricity and replacement costs. I'm not saying to go the RPI3 route, but if you can have one PC do everything, being modular will save a bunch of money and reduce your carbon footprint. Unless you are wishing to play Star Citizen, your graphic needs can be served with the APU.
Actually I had some off time due to a car accident last week, and I got the Xarcade out, hooked it into a spare HDMI with Steam Link. Using a Power Line for network, I was able to play mame and laserdisc games full speed. I had problems streaming my Xbox One with my A10 and Steam link at the same time
but I think it was a crap cable, any way I digress..
I have an A10 in my laptop and I can play pretty much everything on high settings with just the APU, why not in the desktop? Not to mention that the A10 is in the Xbox one and PS4.....
So I guess with Steam Link that could wipe off your total cost of your PC. It is worth thinking about. Valve sells the Steam link for $19.99 on its sales so keep an eye out.
Here is a video showing emulation on the Steam Link: