He most likely wants Superman due to the simple fact he is probobly the most powerful hero on earth at any given time and as a counter to the forces of New Genesis - in particular son Orion.
If Superman didn't exist then obviously his target would be Captain Marvel, it is simply a result of who presents the greatest threat on any given world, and as we have seen there is a Superman on virtually every parallel earth thus far seen. So of course it appears the New God has a particular obsession with that one hero... if you wanted to go further then consider that Darkseid is the Universes God of Evil, while Superman according to many interpretations, not least Grant Morrison's, is a totemic force for good.
The two are natural rivals, and perhaps the surplus of cross-earth Supermen is one of the universes responses to evil like Darkseid's. See Mandrakk as another example.
So would be much as in smallsville, where we saw that darkseid was actually like unto the DC devil, as ultimate evi;/darkness, while Superman, as per dr fate, was the Sentience, akn to be the avater of light and goodness then?