You can find a YouTube playlist here with many of the songs suggested below.
Gathering
The end of the Epistle can invite us to offer praise to God as we gather for worship - the King of the ages, immortal, invisible, the only God. Immortal, invisible, God only wise (CH 132 / MP 327) would be an obvious option here while other songs you could consider include classic hymns such as Praise my soul, the King of heaven (CH 160 / MP 560) and Glory be to God the Father (CH 110) and worship songs like My Jesus, my Saviour / Shout to the Lord (CH 531 / MP 1003 / CCLI), Come and worship Christ the King (Resound) and King of kings (CCLI).
Word
There aren’t many settings of today’s psalm but there are two decent metrical versions to choose from. The foolish claim, “There is no God” (link) is a fairly loose paraphrase in contemporary language and the suggested tune is very singable but some appropriate alternative tunes which are perhaps better known could be Athchuinge or O waly waly. The God who sits enthroned on high (Grace) is a stricter paraphrase but the language may be a little dated for some. Oh, that your salvation and your rescue (PFAS 14A / Lee) is also worth mentioning for those with a good choir. The music is based on the Advent plainchant Rorate Caeli and is relatively tricky for congregational singing although the congregation could sing just the refrain with a choir or soloist taking the verses.
Response
There are lots of popular songs which can link to the Gospel and the Epistle with themes of God’s mercy and repentent sinners such as Amazing grace (CH 555 / MP 31) or it’s popular Chris Tomlin version Amazing Grace (My Chains Are Gone) (MP 1151 / CCLI), You alone can rescue (CCLI), In Christ alone (MP 1072 / CCLI / Getty) and How deep the Father’s love for us (CH 549 / MP 988 / Townend). You could also consider We have heard a joyful sound (CH 249 / MP 730) with it’s repeated chorus of “Jesus saves” or more penitential songs such as Father of heaven, whose love profound (CH 483 / MP 827) and Your grace is enough (MP 1383 / CCLI). The Gospel could link to a version of Psalm 23 such as The Lord’s my shepherd, I’ll not want (CH 14 / CH 15 / CH 16), The Lord’s my shepherd (MP 1008 / PFAS 23F / CCLI / Townend) or The King of love my shepherd is (CH 462).
The opening verses of the Old Testament speak of God’s judgement and you could link to this with songs such as Judge eternal, throned in splendour (CH 264 / MP 395), O Lord the clouds are gathering (CH 708 / MP 509) or even a setting of Psalm 1 such as How blest are those who do not stray (CH 1). You could also link this passage to our lack of care for creation and consider songs such as Hear the song of our lament (Resound), Touch the earth lightly (CH 243) and The garden of the world (Lament for the earth) (Hope).
Sending
The theme of having been saved by the grace of God is a fairly natural sending theme and you could consider using classic hymns such as I will sing the wondrous story (MP 315), O for a thousand tongues, to sing (CH 352 / MP 496) and At the name of Jesus (CH 458 / MP 41) or well known worship songs such as In Christ alone (MP 1072 / CCLI / Getty), Amazing Grace (My Chains Are Gone) (MP 1151 / CCLI), This is amazing grace (CCLI) and Living hope (CCLI).