You can find a YouTube playlist here with many of the songs suggested below.
The God of Abraham praise (CH 162 / MP 645) would strongly root your worship in the themes of the Genesis story while also picking out themes from other passages. While we are still in the season of Pentecost Come down, O Love Divine (CH 489 / MP 89) would also be appropriate. Hosanna / Praise is rising (MP 1221 / CCLI) is a good general gathering song which also sets up themes from various readings around hope and the coming of the Kingdom. If you are using the psalm for a call to worship then you could potentially link it with I love you, Lord (CH 770 / MP 287 / CCLI) and you can also find resonances of the psalm in Awake, my soul, and with the sun (CH 210 / MP 804) and All my hope on God is founded (CH 192 / MP 16).
The Psalm this week is the text for one of my favourite Gospel songs, I love the Lord, he heard my cry (PFAS 116C), setting a paraphrase by Isaac Watts. It might be familiar from a very elaborate version by Whitney Houston but you can hear a fairly straight version in the first verse here which can work congregationally. There is also a beautiful setting, I love the Lord, because he heard (WGRG), in one of the more recent Wild Goose collections. Unhelpfully for our purposes, the way the text of this psalm is split up in CH4 doesn't match the lectionary. However, the two settings are the same metre and stress, so if you want to sing the verses from the lectionary you could add v1 of I love the Lord because he heard (CH 75) to the three verses of How can I ever thank the Lord (CH 76). You can then take your pick of either tune or alternatively use Kilmarnock (CH 69) which is suggested in the 1929 Psalter.
Go heal the sick (WGRG) is based on Jesus’ commission to his disciples in the Gospel to heal the sick and cast out demons while God sends us forth (GIA) also picks this up. The Kingdom of God is justice and peace (Taizé) would make a good prayer response to link to v35 while King of compassion (Satellite) picks up on the line in v36 "he had compassion for them".
The Epistle covers a lot of ground and it’s a challenge to find songs which capture all of it. Some songs which could link in different ways include By faith (MP 1262 / CCLI / Getty), We sing the praise of him who died (CH 405 / MP 738) and My hope is built on nothing less (MP 473 / Hymnary) or the two great reworkings of it - the Kenyan song Kwake yesu nasimama (GSW 34 / GIA) and the popular worship song Cornerstone (MP 1334 / CCLI). Holy Spirit, fill our hearts (CH 611) and Come, Holy Spirit gracious heavenly dove (CH 758) would specifically link to v5 and God’s love being poured into our hearts through the Holy Spirit.
The God of Sarah praise (GIA) is an excellent rewriting of “The God of Abraham praise”, set to the same tune, which allows the woman in the Old Testament story to be brought to the forefront. God has made laughter (CH 764) is also a great response to this passage as it highlights Sarah’s laughter, something we seldom either read or sing about, while God of Abraham lead us (OCP) also picks this up and vv.1 and 2 would link well to this passage.
The Gospel reading is a natural sending passage and Sent by the Lord am I (CH 250) would call on us to be co-creators of the Kingdom here and now while Send out the gospel (CH 681) and Build your kingdom here (CCLI) would also have a missional call in different musical styles. God of Justice (MP 1174 / CCLI) is a great general closing song with a call to "move us into action" while Hear the call of the Kingdom (Getty / MP 1282 / CCLI) takes us explicitly on the journey of hearing and then answering the call to follow. As a fire is meant for burning (CH 252) takes a more corporate approach to mission, naming it as the purpose of the Church.