When did Israel select G-d?
The Siftei Chakhamim explains that the meaning of "Thou hast avouched the L-rd this day to be thy G-d" is:
You have distinguished Him, from the alien gods, etc.
This, according to the Siftei Chakhamim, is also the explanation of when G-d chose the Jewish people to be His people. It was when they accepted the Torah and followed Him. G-d distinguished the Jewish people from the other nations, since they did not accept the Torah etc..
Furthermore, the Daas Zkenim writes:
G–d credits the Jewish people with having traded in any other deities in favour of the invisible Creator, Who had revealed Himself to them at Mount Sinai.
You can view it as a gift: the Jewish people chose G-d from all the other deities they followed. They realised that Hashem is the True One G-d and pushed aside all false deities. In reward for this, G-d made the Jewish people His treasured people (refer to the Daas Zkenim).
Israel had elevated the L-rd G–d to the topmost branch, and the L-rd responded by elevating the Jewish people to the highest ranking nation.
In Maayanah Shel Torah, the HaKesav VeHaKabbalah is quoted in saying that G-d has made the Jewish people exceptional and important by giving them the Torah and mitzvos to keep. This is the distinction that sets them apart from the other "seventy nations".