What do we learn from "Chelki Hashem"?
Ibn Ezra: He was my portion from of old, from all the gods 1 .
Ri Kara: This explains "I will put to my heart, therefore I will hope" (21). Because I chose Him for my portion, to be my G-d, I hope to Him to redeem me from the darkness, incarceration and heavy fetters.
R. Avigdor citing Eichah Rabah 3:8: A Mashal for this is a king who entered a country with nobles and officers. Gedolim of the country were there. Each attached himself to a noble or officer. A Chacham there said, I will attach myself to the king, for all of them can be switched (demoted), but the king is not switched. So the nations serve the sun, moon, idolatries and wood, and Yisrael chose only Hashem.
R. Yonah (Mishlei 3:26): I choose in my world only His Avodah. I have no portion in the world other than fulfilling His Mitzvos with love and fear of Him - "Al Ken Ochil Lo."
I.e. I had no connection to other gods, only to Him. (PF)
What is the meaning of "Amrah Nafshi"?
Rav Sadya Gaon: I say to my Nefesh [that Hashem, my portion, is good].
Ibn Ezra: My Nefesh says to me. Palgei Mayim - this is because You made Your faithfulness to me so strong.
What is the significance of "Al Ken Ochil Lo"?
R. Avigdor: Since this is written after saying that Hashem is my portion, the custom is to say [the Piyut] Ochilah on Yamim Nora'im after Aleinu (in Chazaras ha'Shatz of Musaf).
R. Yonah (Mishlei 3:26): Above (21), it said only "Al Ken Ochil." The hope was only for salvation and Chesed. Here it adds "Lo" - there is hope to be pleasing from Hashem and draw close to Him.