You can find a YouTube playlist here with many of the songs suggested below.
The psalm invites us to give thanks and sing praise to God which would be an appropriate way to gather in worship. Give thanks with a grateful heart (CH 180 / MP 170) would be an obvious choice here while some classic hymns could include Glory be to God the Father (CH 110), Praise to the Lord, the Almighty, the King of creation (CH 124) and Now thank we all our God (CH 182 / MP 486). Some popular songs for band include 10,000 reasons (Bless the Lord) (CCLI) and Let Everything (Praise The Lord) (CCLI) while two less well known songs from Scottish writers worth considering are Let his praise be on our lips (Satellite) and Give thanks to God (CCLI).
Tell what he has done (Grace) sung to Londonderry Air is one of the few contemporary settings of this psalm. Since it appears four times over the course of a few months then you can pick and choose which verses to use each time. Guide me, O thou great Jehovah (CH 167 / MP 201) is not a strict paraphrase but is worth mentioning because it is based on the same narrative of Israel’s journey in the desert.
With so few settings of the psalm it’s also worth considering short songs of praise to God, either as a standalone song or at the beginning and end of a reading of the psalm. Options for this include Praise and thanksgiving let everyone bring (CH 170) where the first verse as a round would work well, Praise, I will praise you, Lord / Je louerai l’Éternel (CH 175), How great is our God (MP 1227) and the Thai song Come and worship (WGRG).
The reign of God, like farmer’s field (CH 343) and Sun, soil and seeds (GIA) bring together both the parable of the mustard seed and the parable of the yeast while To what can the kingdom of God be compared (Carolyn) also includes the pearl. In our lives plant seeds of hope (CH 349) would just link to the mustard seed but puts it in context of various passages focusing on seeds while The Seeds of the Kingdom (Kimbrough) is a more general option. If you are focusing prayers on the kingdom of heaven then The kingdom of God is justice and peace (Taizé) can be a useful response, as is God our Father (Let your Kingdom come) (Resound) which is a setting of the Lord’s Prayer but you could just use the refrain.
The Saviour died, but rose again (CH 425) is a wonderful Scottish paraphrase which covers the final five verses of the Epistle. There’s a wideness in God’s mercy (CH 187 / MP 683) is another classic hymn which could link well while bands might wish to consider songs such as Yet not I but through Christ in me (CCLI), Your grace is enough (CCLI) or You alone can rescue (CCLI). There are some short chants which pick up specific verses and could be used for prayers, Holy Spirit breathe in us (GIA) linking to v26 and Nothing can ever (Taizé) linking to v39.
There aren’t many songs which are suitable to suggest for the Old Testament text. Sometimes wedding hymns are suggested but whether these would work or not very much depends on your approach to this challenging passage.
As with last week, songs about looking towards God’s kingdom would work well for a closing song, including Jesus shall reign where’er the sun (CH 470 / MP 379), At the name of Jesus (CH 458 / MP 41), Sing a new world into being (GIA), The kingdom of God is justice and joy (MP 651), Hear the call of the kingdom (MP 1282 / CCLI / Getty), Let your kingdom come (CCLI) and King of kings (CCLI).