What does this Mizmor discuss?
Radak (citing Pesachim 117a #1): It discusses David.
Radak (citing Pesachim 117a #2): It discusses the days of Mashi'ach and the thanks of Bnei ha'Galus in the singular, as a Klal.
Why does it begin with "Hodu la'Shem"?
Radak #1: It begins and ends with this, due to the praise of the Mizmor and what is said in it.
Radak #2: If the Mizmor discusses David, when he became king, he said 'you must thank Hashem for my kingship, for He did good to you.'
Radak #3: If the Mizmor discusses the days of Mashi'ach, it tells all nations to thank Hashem.
Malbim: All nations should thank Hashem for His Tov and Chesed.
Why does it say "Ki l'Olam Chasdo"?
Radak #1: Hashem does not do Chesed for [only] a year or two, rather, forever - "Chasdei Hashem Ki Lo Samnu" (Eichah 3:22).
Radak #2: h did good for Yisrael, and guarded His Chesed for them forever, i.e. for the many days that they were in Galus.
