1/2 is the size between the roller bits and the 3/32 or 1/8 is the width ,, i think of the roller inside the link plates...? 3/32 is the skinny chain, bmx race bikes and bikes with derailer, mtb etc, 1/8 is single speed , bmx in other words ,
the number of links you will need will depend on the size of the frame and where you position the wheel in the dropouts , but i've always had spares with every new chain i've bought they are always to long , so you'll need to shorten it to the right size , 1/2 x1/8 is the one you want if your going to ride the bike
3/32 need thinner sprocket and freewheel to work properly , race spec bits, most standard bmx sprockets / freewheels are 1/8