I've only been MAME'ing for a few months, but I was a DJ for 10 years. So that part I know a LOT about

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My immediate question would be why put both things in the same cabinet? A karaoke setup has almost nothing in common with a MAME box (other than they both use a PC and have a display). I think you would find it very awkward and would have to make a lot of compromises on the Karaoke side.
My suggestion is to build the MAME box, and also build a karaoke setup. The main component is going to be a stand with the TV/monitor and microphone holders (you want people to be able to look down at the screen and still be able to look up at the 'audience'). You'll want two main speakers, plus a monitor (speaker) pointed toward the singer.
Wireless microphones are a great option, especially if your singers will be drinking. At best they can trip over the wires, at worst they'll pull too far and knock your system onto the floor. A decent microphone mixer is a must have, preferrably with some built in vocal effects. I use Sennheiser or Shure, but you will probably want something cheaper. Audio Technica makes some decent value mics.
There are a lot of different Karaoke software packages out there, with a great range in prices. You'll need to hit Google and figure out what makes sense for you. CD+G is the old standby, and might not be a bad idea for a home system. You don't really need to have everything on an instant-access hard drive when entertaining at home.