If you want to save a little, look for used, off lease, Dells and HPs. You can pick up 4th gen i3 and i5 models for around $100 on ebay. I like the small form factor desktops, not the super thin one with low power CPUs, but the ones that have room for a half height video card. Adding a video card doesn't matter much for MAME roms, but helps out with demeaning front ends.
Most will have Windows 10 Pro installed, or come with a licenses you can use with a copy of it. This gets you remote desktop, and makes admin inside a cabinet a little easier. If you want quick boots and game loading, pick up a 500 GB ssd.