You can find a YouTube playlist here with many of the songs suggested below.
The opening verses of the psalm are a great call to worship and we can echo this in our opening songs. This is a good opportunity to use whatever songs of praise work well for your congregation but some good options to consider include classic hymns such as Praise to the Lord, the Almighty, the King of creation (CH 124), Let all the world in every corner sing (CH 122) and worship songs like Let everything that has breath (MP 1001 / CCLI) and I love you Lord (CH 770 / MP 287). We can also find the language echoed in other psalms with well-known settings such as All people that on earth do dwell (CH 63 / MP 20) or 10,000 reasons (Bless the Lord) (CCLI / MP 1259). Some potentially less familiar songs which are well worth learning are Let his praise be on our lips (Satellite) and From life’s beginning (Let praise resound) (Resound) from two different British worship collectives.
I will always bless the Lord (CH 27) is a good metrical setting of the psalm sung to a beautiful Gaelic lullaby. Taste and see (GIA / PFAS 34B) is a classic from the post-Vatican II style of psalm singing and is a wonderfully soulful setting where you can either have a soloist take the verses (ideally someone with a jazzy voice who can have freedom to improvise a little) or else just use the chorus for a responsorial setting. Psalm 34 (Taste and see) (CCLI) is a good option for those looking for a worship song style although this could be done in a whole range of styles from contemporary folk through to Gospel. There are also a couple of other options for singing the psalm responsorially including the short Kenyan song Bless the Lord (CH 756) and the Taizé chant Bless the Lord my soul (Taizé).
When Jesus the healer (CH 350) is a lively song which looks at many different stories of healing in the Gospels while Jesus Christ is waiting (CH 360) has verses about different aspects of Jesus’ ministry including one about healing. Lord of life, we come to you (CH 782), O Christ the healer we have come (CH 717) and We cannot measure how you heal (CH 718) turn the focus onto our prayers for healing in ourselves and people we know. Worship songs speaking about healing was a bit of a gap but some more recent ones have focused more on this including Miracles (CCLI), God with us (CCLI) and Impossible things (CCLI).
The Epistle continues its focus on Jesus as a high priest and songs from previous weeks are still relevant here including Come and praise him, royal priesthood (MP 87), Where high the heavenly temple stands (CH 451), Before the throne of God above (CH 466 / MP 975) and High Priest (CCLI), although the latter is probably more suited to a soloist than a congregation. You could also consider songs which hint at the perfection of Jesus such as Christ, whose glory fills the skies (CH 578 / MP 79) and Jesus, name above all names (CH 774 / MP 375).
Penitential songs such as Father of heaven, whose love profound (CH 483 / MP 827), Your grace is enough (MP 1383 / CCLI) or Come, O Lord, and set us free (WGRG) could be appropriate for the Old Testament as Job repents. There is also a specific reference to “dust and ashes” which could link to Beautiful things (CCLI) (“You make beautiful things out of the dust”) or Ashes (CCLI) (“From the ashes you call my heart to life”). You could also use songs which speak of our faith that God will be there for us at the end of all our troubles such as Goodness is stronger than evil (WGRG), My life flows on in endless song (How can I keep from singing) (CH 565) or Held by this hope (Satellite).
For all of the readings it’s appropriate to finish with songs of praise to a God who is ultimately faithful to us whatever we have gone through. Some classic hymns you could us include Praise my soul, the King of heaven (CH 160 / MP 560), Be thou my vision (CH 465 / MP 51) or O for a thousand tongues to sing (CH 352 / MP 496), particularly with its reference to healing the blind in v5, while Cornerstone (CCLI) and By faith (MP 1262 / CCLI / Getty) are some more contemporary options.