A multi-speed chain is 3/32", so it can be used if the chainring and cog are also 3/32". The advantage of using a regular 3/32" single-speed chain is that the pins are a bit longer, such that they protrude beyond the outer chain link plates, making it a bit easier to assemble the chain.

There is no advantage in using a crank with attached chainring, since you cannot remove it to change the gearing or replace it when it wears out without replacing the complete crankset. Usually you find chainrings that are swaged onto the crank arm in cheaper cranksets, and better quality cranks typically use separate chainrings that bolt onto the crank arm spider.