Covenants in the Torah

In the weekly Torah portion, we have entered the territory in which most of the covenants between God and humans were forged.

The first covenant is forged using the rainbow as a sign: Genesis 9:12, 15
The rainbow serves as a reminder that all of humanity will never again be destroyed with water. This covenant is between God and all of humanity

The second covenant is made over the mark of circumcision: Genesis 17:10-11 (read the whole chapter!)
This is between God and Abraham's descendants and household (Abraham passes on the tradition of this covenant to his son in Genesis 21)

The third covenant is created through the Shabbat: Exodus 31:13-17
This covenant is between God and the Children of Israel.

The rainbow, circumcision and Shabbat serve as a sign (אות) of God's role and involvement in the world. Circumcision and Shabbat serve as a mark of the special connection the Jewish people have with God.

On one hand, this is a very cursory view of these covenants, but on the other hand, for the God-fearing believer, these are very deep concepts.

The rainbow is external - it is for all of humanity.
Circumcision (as a covenant) is a one time deal which is difficult when it happens, but you don't really notice it beyond that. It is for Abraham's descendants and his household, not as general as the covenant of the rainbow.
Shabbat is, for the uninitiated, more difficult, more taxing, more long-term commitments, and it involves the entire body, on a weekly basis, and is exclusively for the Children of Israel.

We go from very general to very specific. What does this say about God? What does it say about different peoples?