If you are searching your local Craigslist for an existing arcade game to house the multi 60-in-1 board, be sure that it is a vertical jamma game. Search the KLOV.com database (toki as an example) and find out it's monitor orientation and conversion class. If it says "vertical" that means the monitor is mounted vertically in the cabinet like Dig Dug, Pac-man, or 1943 as examples.
If the conversion class says "jamma" that means it shares a universal pin out with all other "jamma" boards. This was the main pin out used beginning the in the 80's. So only Jamma boards can be swapped in to it's wiring harness. Equivalent of trying to place a Sega Genesis cartridge into a Super Nintendo console, if the little pinouts don't match up, then they can't be swapped.
By buying a vertical, jamma (hopefully that has two buttons as well) cabinet you are pretty much gonna spend the least amount of effort in order to play the games right away with a 60-in-1 board. Simply pull off the existing board inside and plug the new one back on. Occasionally, depending on the monitor inside, you may have to clip a sync wire.
Other boards like the Blue Elf 309-in-1 were designed with horizontal monitors in mind for playing newer titles, so you'll need a cabinet with horizontal mounted monitor. But it should be the same plug in and play Jamma harness needed inside.
Search the game selections available for each multi board to decide which games you like best to play. That will dictate which kind of monitor style cab you should buy.
Of course. barring a bunch of mind-numbing details, this is the overall basics behind the mulicade scene.