Both Ashkenazim and Sephardim add various psalms to Pesukei deZimra on Shabbath and on holidays. Rambam mentions Psalm 92, 136, 121–124, but are there any sources why these particular psalms were selected and why in their particular order?
Levush (OC 281:1) writes the reason they are read is either because they speak about Creation, which was completed on Shabbos, or they speak about the giving of the Torah, which was given on Shabbos. He also notes that they are grouped by these subjects, rather than by the order in which they were written.
He then goes on to explain the precise order:
Psalms 19: It is the first that deals with Creation.
Psalms 34: It is the first to speak about Shabbos.
Psalms 90: Also speaks about Shabbos.
Psalms 91: To save us from evil spirits that roam on Friday night.
Psalms 135: Speaks of the giving of the Torah.
Psalms 136 (The "Great Halel"): It contains 26 mentions of the phrase "For His kindness is everlasting", corresponding to the 26 generations from Creation till the Giving of the Torah.
Psalms 36: It is only after The Great Halel that the righteous will praise Hashem for his great kindness. Psalms 92: Further praise to Hashem.
Psalms 93: Signifies the completion of the Creation, when Hashem sat on his Throne of Glory.