"Restore" to me means to return it to original spec, which would mean a geared build with the original black-and-gold components. If you're willing to pay top dollar it shouldn't take long to track down the original-spec parts; if you're needing to keep the budget low you could be hunting for a while.

If you're not looking to restore it, then you're just looking to build it up. If you want to build it with vintage period-correct but not original-spec equipment, you could go either geared or fixed; ditto if you want to mix vintage and modern equipment. Keep in mind the vertical drops make chain length/tension difficult building fixed unless you use a modern rear wheel w/eccentric hub/axle, or install a modern Phil eccentric bb. It's not impossible to go fixed without an eccentric hub or bb, but it can be a pain.

Do check the frame for alignment and cracks, aluminum frames are less likely to bend than steel but more likely to crack. The extra hole drilled into the rear drive-side dropout for the makeshift wheel stop would be at least a minor concern to me. There's a fair amount of beef in the dropouts, but the hole is in an unusual spot (compared to, say, a rack/fender hole). If you don't see any small cracks radiating from the hole it likely won't be a problem, but it's generally not a great idea to be adding holes in random spots that normally don't get drilled.

Just as a FWIW, hearses in Japan are black-and-gold like just like the Black Lightning. SunTour Japan staffers never really understood the appeal of the color scheme, some of them were slightly creeped out by the whole idea. The Black Lightning was usually internally referred to as "the hearse bike," and the color scheme was called "the hearse finish." I always thought the Black Lightnings looked cool built up.