First off I like the way S:TAS portrayed Darkseid, it really is the true version of the character when it comes to Superman. I would develop a story similar to this version, except I would show Darkseid as more of a villain than anything else.
It would start out with the theme, pride, Superman's return to Earth has become overconfident and full of pride of the acceptance of his return, much like Peter in Spider-Man 3. This means Lois is back in love with him, the world is generally praising Superman for his return and such. Suddenly being the jealous type, Darkseid sees this and is disgusted, but slighly jealous of the praise Superman has earned. Using the over dramatized reactions of humanity, he assumes that the Anti-Life Equation is in them because they are so easily impressed. He decides he must act to get the formula.
As Superman begins to enjoy and prideful in life, something happens that causes him to change his tune. A disease epidemic breaks out and causes the deaths of many hundreds of people. Later research finds it to be a Kryptonian virus that Superman may have brought back with him in SR. Superman soon begins to be blamed for the break out and is soon isolated as an alien.
Lex Luthor takes advantage of this and begins building credibility, from a person who seems least likely to get it, and bashes Superman for his bringing the virus to Earth and warns humanity of what else could happen. What's worse is Lois, and several others at the Daily Planet are infected and hospialized.
Of course this is no ordinary disease, it causes what could be similar to the results of a Bird flu break out all over the world. Civil strife, meidcal shortages, vandalism, rioting, and all out chaos erupt on a global scale. Superman blames himself and decides to isolate to the Fortress of Solitude.
Eventually Darkseid reaches out and promises a cure for the epidemic on a distant alien world. He then forces Superman to vow to never return to Earth and hand the cure to him for the sake of humanity.
Superman goes to the planet to find the cure, while Darkseid's forces surround Earth and begin pressing in an invasion. Darkseid lands and begins telling humanity that he has a cure. He then repairs the damages left behind by the disease, which he does not reveal he created. He then gets the trust of humanity and his fleet moves in.
At the same time, Darkseid makes a deal with Lex Luthor to give him weapons in turn for giving loyalty from the crowd he has gathered from degrading Superman. Once he has their control, he personally severly beats Luthor and forces the crowd to give in to him.
Peaces turns to chaos as Darkseid begins rounding up humans and searching their minds for any trace of the anti-life equation. He kills many thousands in the process and kills anyone who resists inspection and taking oath to Darkseid. He also kills random humans as an example to resisting his rule. Several large cities are destroyed in the process. Hell on Earth has erupted.
Superman returns to Earth after finding the ingredient which Darkseid told him to get and is betrayed. Darkseid informs Superman of the truth and tries to have him killed the second he returns. He survives and realizes he must help humanity.
Superman eventually must ally with Lex Luthor, Lois and the rest of humanity to fight off the armada which has gathered over Earth, no matter how much they don't want to. Darkseid and humanity then have a large battle and much of the fleet is destroyed. Superman Darkseid brawl in a personal fight.
Just as Superman is about to kill Darkseid, as he is infamous for nearly doing, Darkseid takes advantage of the oppotunity and kills several million people in a large device that levels a large part of Metropolis and kills many thousands to make a personal mark not to mess, with him, he then escapes back to Darkseid seemingly undefeated.