According to the Tanach (Hebrew Bible), Jews are the chosen people. In this context, 'chosen' refers to Jews having been chosen to follow the teachings of the Tanach.

They don't think, they know who they are. They are the Jews, God's Chosen People!

It means that while the Jews were in the desert, God took the holy bible, the Torah, So when God went to the Jewish people, the Jews answered, "Of course we want your holy Torah!" That's what it means to say that the Jews are God's chosen people!

What riches? There are poor Jews, middle class Jews, upper class Jews, just like there are with ALL PEOPLE. Chosen people refers to being chosen to obey the 613 commandments of the Torah, like keeping kosher and observing the shabbat. Non-Jews have commandments too, and their own covenant with G-d. They are supposed to observe the Noachide laws.

See Exodus ch.19.