You can find a YouTube playlist here with many of the songs suggested below.
The Psalm is a good starting point for a Call to Worship with its celebration of God’s goodness and greatness and God’s holy ways are just and true (Jubilate) would be a good opening hymn directly inspired by it set to a well known tune. You could also use many general songs on this theme with well known options such as Great is thy faithfulness (CH 153 / MP 200), Sing to the Lord a joyful song (CH 184 / MP 929), Goodness of God (CCLI) or Good, good Father (CCLI). Some less well known ones worth exploring are the exuberant Mexican song Let’s sing unto the Lord (CH 176) or We rejoice (Satellite) from a Scottish songwriting collective which would be quite simple to pick up. If you are focusing on the Gospel passage then Come and find the quiet centre (CH 716) would link to this as we open ourselves to God’s presence in our worship.
Psalm 111 doesn’t have many settings although if you didn’t use God’s holy ways are just and true (Jubilate) as an opening hymn then this is an option here. In this situation I often turn to the Scottish Psalter and Praise ye the Lord: with my whole heart (Hymnary) is in Common Metre so there are many options. However, watch that v2 has an extra syllable at the end of some lines so I would probably use Stroudwater which helps with this. In Hebrew this is an acrostic psalm, where each section starts with a letter of the Hebrew alphabet in order. All my heart will praise the Lord (An Alphabetic Psalm) (CCLI) is interesting in that it does this in English. It has quite a rare metre but could be sung to Liebster Jesu with four Alleluias at the end of each verse. I will give thanks (GIA) is one of the few contemporary settings, written in a jazzy style for choir with a congregational response. The arrangement makes it quite complicated for use in most congregations but I would be tempted to use the first three verses that are all set to the same tune along with the refrain. Alternatively, this is a psalm where you can always use your favourite Alleluia to sing it responsorially.
God of the prophets! Bless the prophets' sons (Hymnary) is probably the song which links most directly to the Deuteronomy text, with a focus on the succession of prophets, priests and apostles. We sing to you O God (link) is a song about the wider context of the Israelites at this place in the Old Testament and their trust in God. Looking at more general songs, One is the body (CH 679) speaks of the different callings God’s people have including “some to be prophets”, God has spoken by his prophets (Hymnary) touches on the place of prophets while Speak, O Lord (MP 1350 / CCLI / Getty) could link into their role and how people should respond to what they hear from God through them.
Brother, sister, let me serve you (CH 694 / MP 1261) would be a way to reflect on the Epistle from the perspective of our love and support for each other while Ubi caritas (CH 801) is an 8th century text about God’s love set here in a beautiful Taizé chant that is easy to sing in two parts. We are all one people (MV 141) and We believe in one God (Unshakeable) (Resound) could both tie in to the focus around v6 of there being one God and one Lord. Be the centre (MP 1076 / CCLI) or Jesus before me (CH 576) are more general songs about Jesus being at the centre of all we do.
Silence! Frenzied, unclean spirit (link), which can be sung to Ebenezer, was written to fill the gap of songs which speak about Jesus casting out demons as in today’s Gospel reading so would be the song with the most explicit link. 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 which could be appropriate since this is the first public demonstration of it in Mark and in this lectionary year. 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.
There is no text jumping out as an obvious way to end the service so consider songs relating to the text you preached on as suggested above, or use something more general. Like with the gathering, songs about God’s goodness and greatness could work, but with more sense of a response and dismissal. O for a thousand tongues to sing (CH 352 / MP 496) is always a great song to finish with and connects with healing in v4/5 as does Son of God, eternal Saviour (CH 468) in v1, while also focusing on living for others in v2 which can link with the Epistle. By faith (MP 1262 / CCLI / Getty) takes us on a journey through faith throughout the Bible ending with a call for us to “walk by faith”.