You can find a YouTube playlist here with many of the songs suggested below.
Gathering
The psalm is a strong gathering text today, with God summoning the earth, calling to the heavens, and shining in perfect beauty. A setting of it such as God the Lord, the King almighty (CH 39) could work well as an opening hymn while songs such as Jesus shall reign where’er the sun (CH 470 / MP 379), Creation sings the Father's song (MP 1268 / CCLI) or Bright morning maker as your sun breaks through (CCLI) (sung to Engelberg or Sine Nomine) would pick up on the journey of the sun and people and all the earth singing praise to God.
With the focus on the Transfiguration today the line “let light shine out of darkness” from the Epistle can give us another starting point and songs such as Here in this place new light is streaming / Gather us in (CH 623) and Be still for the presence of the Lord (CH 189 / MP 50) fit very well into this theme. Imagery relating this verse and link to the Transfiguration can also be found in songs such as Way Maker (CCLI) (“Light in the darkness my God that is who You are) and Open the eyes of my heart (MP 1100 / CCLI) (“To see You high and lifted up, shining in the light of Your glory”).
Word
There are relatively few settings of Psalm 50 but if you didn’t use God the Lord, the King almighty (CH 39) as an opening hymn then it is worth considering. Other metrical settings you could us are The mighty God with power speaks (PFAS 50A / Hope) sung to Kingsfold and The Lord of the ages, the Father of years (CCLI) vv.1-3 which could be sung to Slane. Let the giving of thanks (WGRG) can either be sung in full with the chorus and verses, or else the chorus could be used to sing the psalm responsorially.
Response
There are a number of songs which reflect specifically on the story of the Transfiguration, mostly by contemporary hymnwriters, including Bright the cloud and bright the glory (CH 353), Jesus, on the mountain peak (STF 259), Transform us as you, transfigured (Hymnary) and Transfigured Christ, none comprehends (STF 261). There are also some hymns which have verses about the Transfiguration amongst a range of stories from the life of Jesus such as Out of the flowing river (CH 335) and Christ is our light! the bright and morning star (CH 336). A left field option could be The Transfiguration (link) by Sufjan Stevens. This wasn’t written as a congregational song but could either be played as a reflective piece or actually some congregations might find they could join in as the music is fairly predictable. You can find a theological reflection on this song here.
Some of the songs mentioned in the gathering section could be used as more general responses while other options could be Be the centre (MP 1076 / CCLI) and Turn your eyes upon Jesus (MP 712 / Hymnary) which has been popular with quite a few worship leaders recently. There are also a number of short chants relating to the theme of light which could be used for prayer responses such as Kindle a flame (WGRG), Lumière de Dieu / Come light, light of God (CH 784) and La ténèbre / Our darkness is never darkness in your sight (Taizé) and The Lord is my light (Hymnary).
Sending
You, Lord, are both Lamb and Shepherd (CH 355) and The voice of God goes out to all the world (CH 283) could be good closing hymns which link the Transfiguration to God walking alongside us throughout life. How great is our God (MP 1227 / CCLI) would also link well with references to “Clothed in majesty” and “He wraps himself in light” while the imagery in Lord the light of your love is shining / Shine, Jesus, shine (CH 448 / MP 445) also links well. You could also use some more general songs about Christ bringing light into the world such as God of revival (CCLI), Christ is the world’s true light (CH 456) or Longing for light, we wait in darkness / Christ be our light (CH 543 / MP 1201).