Long before there were CLASS-D mini amplifiers on the cheap, I found a 2.1 speaker setup intended for the N64 on clearance at a ToysRUs and just positioned the satellites behind the speaker cutouts and put the main amp/sub inside of the cabinet. It was hacky, but sounded great and couldn't be beat for the money.
That stated, there are a lot of good options now in the way of cheap mini amps and plenty of speaker options to roll your own system for not too much money. If the cabinet will double as a jukebox, go wild. Otherwise, you don't need anything expensive or fancy for old arcade games. Very few of them were even in stereo, let alone in high fidelity. But I do recommend some sort of larger, low-range driver inside the cab to give the smaller speakers a bit more oomph and fill the sounds out better.
There's no shame in using a PC 2.1 audio setup, so long as it sounds good, can be made to physically fit your space, is hidden from view and checks all your preference boxes. Hot melt and/or plastic plumbing strap and a few screws can help in mounting the satellites.