You can find a YouTube playlist here with many of the songs suggested below.
Gathering
The opening verse of the psalm is an invitation to give thanks and praise to the God who loves us and you could consider songs in a range of styles including Great is thy faithfulness (CH 153 / MP 200), Praise my soul, the King of heaven (CH 160 / MP 560), Give thanks with a grateful heart (CH 180 / MP 170), 10,000 reasons (Bless the Lord) (CCLI), Let Everything (Praise The Lord) (CCLI) and Let his praise be on our lips (Satellite).
Word
It is good to give thanks to you, Lord (PFAS 106A / Hymnary) would work well for the psalm with a solo or small group singing the verses and the congregation joining for the chorus while Banks of the Nile (GIA / link) and Give thanks to God, for He is good (Grace) would be other good options. Give praise and thanks unto the Lord (CH 70) is a solid option for this psalm generally but unlike the previous suggestions doesn’t include the later verses which link to the Old Testament. Give thanks to God (CCLI) would be an interesting option for singing the psalm responsorially if you were to just use the lines “Give thanks to God” and “His never ending love is steadfast and sure” as a refrain.
Response
A king planned a party (Carolyn) is a good story song for the Gospel while Your hand, O God, has guided (CH 511 / MP 705) is a classic hymn which references this story in v2. You could also use songs about the kingdom of heaven such as The kingdom of God is justice and peace (Taizé), The kingdom is yours (Common) and O holy, heavenly kingdom (Hymnary).
Stand O stand firm (WGRG) would link well to the Epistle as it draws on the language in v1, as does Stand firm in faith; unfailing is the Lord (GIA). Wait for the Lord (CH 276 / Taizé) would link the call to stand firm with the statement that the Lord is near in v5 while in v6 we are told to bring our concerns to God in prayer and What a friend we have in Jesus (CH 547 / MP 746) or Bring it all to me (Fischy) would respond well to this. Finally, Na jijoho / Peace be with you (GP 3 / MV 224 / GIA) would echo the blessing in the final verse.
Jesus call us o’er the tumult (CH 509 / MP 359) is a classic song which links well to the Old Testament, potentially not singing v2 so as to put the focus on v3 and being called “from the worship of the vain world’s golden store”. Other songs which speak about the temptations of false idols include Cast down, O God, the idols (Hymnary), O, the love of my Lord is the essence (STF 431), Give us clean hands (CCLI) and Jesus name above all names (CCLI) - the latter being the recent release by KXC Worship and not the song from the 70s. You could also consider more general songs of penitence such as Dear Lord and Father of mankind (CH 485 / MP 111) or Teach us, O loving heart of Christ (CH 488).
Sending
The Gospel can lead you to end with song about looking towards God’s kingdom. ‘Thy kingdom come!’ - on bended knee (CH 473) is a classic option while The kingdom of God is justice and joy (MP 651) and Sing a new world into being (GIA) are more recent hymns and Hear the call of the kingdom (MP 1282 / CCLI / Getty), Build your kingdom here (CCLI) and Let your kingdom come (CCLI) are good options for bands.