Most teams will use their best starter for Opening Day, the second best on the second day, etc. through the rotation.
Except when other factors intervene; for instance, the White Sox ace Chris Sale pitched the Sox' fourth game, because injuries meant that he wasn't ready for Opening Day. And the Pirates' Francisco Liriano, who pitched Opening Day, took paternity leave and pitched the fourth game of the following series.
My understanding is that while aces are better than "backenders"on the same team, they don't necessarily have better records, because they pitch against other aces, while backenders pitch against other backenders. Does this hold through a season, or do "rotational" factors allow aces to sometimes pitch against backenders? And do aces' win-loss records in fact, improve, when they are pitted against backenders?