Granted, I haven't read the Horus Heresy series yet (although I do intend to) but I was told that the Emperor made a bit of a deal with the Chaos gods when he made the marines. Something about giving up all or part of humanity. He reneged on the deal, thinking that his marines would be able to claim victory over the forces of Chaos, never thinking that Chaos might use his own creations against them.
If this is true, I think that it wouldn't matter who the Primarch was, the Heresy would've happened. And I think that the gods would have targeted the Warmaster no matter who it had been, and that they would have successfully turned him away from his cause.
Had they targeted Sanguinius, I think that it would have been much the same for the marines, but much more severe for the Humans. He would've pulled about half the legions (maybe more than Horus as result of him being better liked), but far more of the human population would have rallied around him because he was more loved, and because he looked like a divine being. The Heresy would've taken on a far more religious point of view than it actually did.
If they hadn't been able to corrupt Sanguinius, I think that there would have been small rebellions on the scale of Badab. However, as the Empire grew, I believe the situation would become more and more like Rome. The laxity which allowed Magnus to not only survive but also to flourish in his dark arts would have meant that Chaos would have an easier time swaying not only the mortal citizenry, but also the marines. Remember that a lot of the institutions and rules that are adhered to in the Empire today, would have never come about if not for the Heresy.
We'd have also probably wiped out the Eldar, leaving Chaos to run free in the galaxy.