When did Hashem acquire His congregation?
Rashi: Before creation of the world - "Ma'on Atah Hayisa Lanu; b'Terem Harim Yulado" (90:1-2).
Radak: When He took them out of Egypt; they were slaves, as if they were sold to Egypt. So acquire them now, from this Galus!
Malbim: In the days of the Avos and Shevatim. You promised to be Elokim to their seed - it is proper not to abandon Your acquisition!
Why does it say "Shevet Nachalasecha"?
Radak #1: All the Shevatim are mentioned as one (singular), for they were special in Egypt amidst another nation, and they are Hashem's inheritance called on His name.
Radak #2: When He acquired them from being slaves, they were called His inheritance - "v'Hem Amecha Nachalasecha Asher Hotzeisa b'Chochacha ha'Gadol" (Devarim 9:29).
Malbim: Later, You redeemed the Shevet of Your inheritance, when strangers took possession of Your acquisition. If so, You should redeem them also now!
Why does it say "[Har Tziyon] Zeh Shachanta Bo"?
Rashi: This is like Asher Shachanta Bo. Also "Zu Chatanu Lo" (Yeshayah 42:24) is like Asher Chatanu Lo.
Radak: You redeemed them from Egypt until You brought them to Har Tziyon, on which You dwelled. And so it says "Am Zu Kanisa; Tevi'emo v'Sita'emo b'Har Nachalasecha Machon Shivtecha" (Shemos 15:16-17). It says "Zeh" because Har Tziyon is known, or because this Mizmor was said there.
Malbim: Since You dwelled in it, You should illuminate Your face on Your desolate Mikdash, for Your sake.