The problem with using an ATX power supply is that it has a connector that registers the power-button through the motherboard, but the 60-in-1 doesn't support this. You can short the two pins together that wait for the signal (or snip and tie the wires together) if you want. It's easier to just get a power supply that turns on when the switch on the power supply itself is turned on.
It's cheaper (usually) to just use a switching power supply than an ATX or AT. The only difference is you would have to tie the wires from the JAMMA connector to the lugs and tie 120 A/C into the switcher. If that sounds too complicated for you, go with the PC-style power supply of your choice...