1. Either way should work. Personally I MAME'd an existing cab, so I used the power switch method, wired the PC switch to the cab switch and just set it to shut down when I pushed it.
2. Some of those games are 8-way, so you will need 8-way sticks, or sticks that can switch between 4 and 8 way (several options for this).
Looks like a cool cocktail project!