Parshat Tzav lists the various types of sacrifices one would bring. The first one described is the Olah, which is completely sacrificed, with no opportunities for the priests to partake, and he brought twice a day, every day (6:2). This is followed by the Micha, Chatat and Asham offerings. The last one described is the Shlamim, given as an expression of gratitude (not related to any sin), and that is shared with the Kohen and the donor as well (7:11-15). Is there a reason for this particular order?
It could be that the sequence is a practical lesson for us: Relationships need to start with constant selfless giving. Parents are introduced to this form of giving early on, even before the child is born, but it’s true for all our relationships, with friends, spouses and G-d. If you follow that with devoting a portion of your efforts to others (Mincha offerings), followed by apologizing when we do something wrong (Chatat and Asham offerings), we’ll hopefully get to the point of thankfulness (Shlamim offering) and those around us for all that we have been blessed with.