To You, O Lord, I lift up my soul (v.1) — David begins by appealing to God on the basis of their relationship. The opening verse is an idiom used elsewhere to express deep longing, desire and need, as in Deuteronomy 24:15 and Jeremiah 22:27. The first reference (Deuteronomy 24:15) is an especially significant parallel, since David refers to himself in v.16 of this psalm by the same term, as a “poor man” — referring primarily to his psychological-emotional state (see vs. 16-17) and socially humble origin (cf. also 1 Samuel 18:23). — Wechsler, pages 80-81.
his descendants shall inherit the earth (v.13) — anticipating God’s covenant promises to Israel — see Psalm 37
David goes on to specify precisely what he desires God to provide for him, which provision includes not only deliverance from his enemies (vs. 2-3, 15, 19-20), but also emotional=psychological relief from his loneliness and the troubles of his heart (vs. 16-17) as well as — and most emphatically of all — the spiritual triumvirate of forgiveness (vs. 7, 11, 18), instruction in the ways/paths of the Lord (vs. 4-5, 8-10, 12, 14), and a sense of proximity, or intimacy to God (vs. 14 — the meaning of the Hebrew here rather than “secret”). — Wechsler, page 81.
covenant (v.10) — the first time this word is used in Psalms
prosperity (v.13) = that which is fundamentally good, not material prosperity.
show (v.14) = cause to know
David’s concern was ultimately for the provision of what was best for his people, and in his petition David therefore emphasized that which he needed most to do his part in leading them along that path of what was best (hence his repeated reference to God’s “path(s)” and “way(s)” in vs. 4, 8-10 and 12). Yet in order for anyone to even begin along that path, God must provide that which is the most fundamental of all needs — to wit: redemption from sin, the penalty for which can only by paid by God. Hence David implores God to redeem Israel, employing the verb that specifically denotes the paying of an outstanding debt — and which elsewhere denotes the work of complete spiritual-physical redemption from which man is disqualified and which only God, in His grace, can supply (see Psalm 49:7-8; Isaiah 1:27; Jeremiah 31:11). — Wechsler, page 82.