You can find a YouTube playlist here with many of the songs suggested below.
There is a broad theme this week of faith in God in challenging situations so general songs about faith and trust in God could be a good way to begin. Great is thy faithfulness (CH 153 / MP 200) has the promise of “strength for today and bright hope for tomorrow” while Praise to the Lord, the Almighty, the King of creation (CH 124) praises the Lord who “shields you from harm” and “with blessing and power will defend you”. There are a couple of songs from Scottish songwriters you could consider, such as Give thanks to God (CCLI) with it’s refrain of “His never ending love is steadfast and sure” and Let his praise be on our lips (Satellite) which has us praising God in the good and the bad times of life. If you are focusing on the Gospel then O God, our help in ages past (CH 161 / MP 498) could link through God as our “shelter from the stormy blast” while Oceans (CCLI) could also be an option, although personally I don’t feel it is suitable as a congregational song unless everyone knows it very well.
Regular readers will know that I’m a big fan of Wendell Kimbrough and The hope of the poor (Grace / Kimbrough) is a great option for the psalm this week, with a tune that is very singable for congregations and a Gospel feel which works well with the text. God shall endure for aye; he has (CH 6) is a Scottish paraphrase which only gives us a few verses from the reading but it is probably enough to capture the essence of it, although of course if you have a psalter you can add in the appropriate verses. Come, sing to God with all your heart (PFAS 9C) is another option worth tracking down if you would like a metrical setting - the tune Morning Song is widely known but it is a Common Meter tune so there are many options available.
There Gospel reading has some wonderful less well known songs which are worth considering such as the beautiful short chorus Calm to the waves (link / GIA) with an option of two different tunes (the one by Thomas Pavlechko is particularly good), Into the deep (Gordon) which has a bit of a folky feel and a particularly lovely chorus, and The man who calmed the sea (CCLI / Townend). You could also consider songs about faith in God in times of trouble such as When the storms of life are raging (CH 570) or Safe in the shadow of the Lord (CH 55).
As with last week, By faith (MP 1262 / CCLI / Getty) would link with the Epistle, and particularly the speaking “as to children”. Strength to trust (Satellite) could tie in with the list of hardships which are faced by “servants of God”. You could also link to the final verse with I give you my heart (CCLI) or Give thanks with a grateful heart (CH 180 / MP 170).
Who would true valour see (CH 535) has a direct link to the Old Testament story of David and Goliath with it’s reference in v2 to “he’ll with a giant fight” while the classic Lutheran chorale A safe stronghold our God is still (CH 454 / MP 2) speaks of God’s power compared to the “force of arms”. Everlasting God / Strength will rise (CCLI) would be a more general reflection on finding strength in God and on that theme you could also consider short songs such as Stand O stand firm (WGRG) or Goodness is stronger than evil (WGRG).
For intercessions you might want to link to the psalm and I have sometimes used Lord you hear the cry (Resound) as a way to sing intercessions for those who are crying out to God for help in times of trouble.
All of the readings speak of our need to trust God in times of trouble and a final song can praise God for being there in those times. Eternal Father, strong to save (CH 260 / MP 122) and Will your anchor hold in the storms of life (CH 737 / MP 770) would be two classic hymns which particularly link to the Gospel, with We have an anchor (CCLI) a reimagining of the latter, while My lighthouse (CCLI) is a popular worship song which is also partly inspired by this text. More general songs on this theme could be There's nothing that our God can't do (CCLI), All my hope on God is founded (CH 192 / MP 16) or One more step along the world I go (CH 530 / MP 1346).