Offerings: Peace to Sin

I found the first 4 chapters of the book quite punctuated with the theme atonement. Now, since we all know that, I wonder if we can also agree that the perspective of atonement from God's children in these passage might seem/feel very encompassing. As in, God is actively working to make sure that His people will all have access to full atonement. I think it is interesting to see the sacrifice move from burnt offerings to grain, from grain to peace and from peace to sin. Also within each set of strict guidelines there is a way for poor or rich to come. In the first chapter he moves down from bulls all the way to a bird. Who could not get a bird is the point I gather. From this there stems the idea that all need to bring offering to God. One, because he asks and is worthy. And Two, because we are all in need of what He offers. Past this idea of general offering for offering sake I see the differentiation in having peace with God and being viewed as righteous by God, even if only for a moment as an Israelite.
I think further reading will help to illuminate what I expect to find in the differences between offerings of spiritual atonement and offerings of law. Which is why, I think, Jesus came to fulfill the law not abolish it. Glad to chat. Thoughts...?