You can find a YouTube playlist here with many of the songs suggested below.
This is the Sunday after Ascension Day so it would be very appropriate to begin with songs which celebrate this and call us to worship with well known options including The Lord is King lift up your voice (CH 129 / MP 656), Rejoice! the Lord is King (CH 449 / MP 575), Jesus shall reign where’er the sun (CH 470 / MP 379) and My Jesus, my Saviour / Shout to the Lord (CH 531 / MP 1003 / CCLI). Christ triumphant, ever reigning (CH 436 / MP 77) is a fabulous contemporary hymn that is well worth introducing if your congregation don’t know it. I have some reservations about how large the range is (two octaves) for a congregation in All hail King Jesus (CCLI) but it does a good job in taking us on a journey from Easter to Ascension and the different musical sections are all strong and catchy. Clap your hands, all you nations (PFAS 47D / GSW) is a joyous setting of Psalm 47 (which was the psalm for Ascension Day) from West Africa which would be very easy to pick up.
There are not many options for the Psalm and the most useable is probably Let God arise! his enemies, be gone (Jubilate / PFAS 68C), which is suggested to be sung to Song 46 but Chilton Foliat or Woodlands could also work if you have an even number of verses. Alternatives could be Arise, O God, in wind and fire (Jubilate) in more contemporary language or God shall arise, and by his might (Grace) in more traditional language.
The reading from Acts covers the Ascension story and some classic hymns to link to this could include Hail the day that sees him rise (MP 202), Lift up your hearts, believers (CH 446) and Blessing and honour and glory and power (CH 441) while Open the eyes of my heart (MP 1100 / CCLI) or All hail King Jesus (CCLI) are some options for bands. You, Lord, are both Lamb and Shepherd (CH 355) would be an interesting contemporary hymn as it explores Christ being both human and divine while if you want a more reflective option then you could also either of the Taizé chants Jesus, remember me (CH 775 / Taizé) or The kingdom of God is justice and peace (Taizé).
You could link to the Gospel with songs which speak of the glory of Christ such as The head that once was crowned with thorns (CH 438 / MP 647), God, we praise you. God, we bless you (CH 120) and All heaven declares (CH 426 / MP 14). You could also pick up on the prayer for unity at the end of the reading with songs such as Bind us together, Lord (MP 54), In Christ there is no east or west (CH 624 / MP 329) or We are one in the Father’s love (CCLI).
What a friend we have in Jesus (CH 547 / MP 746), My life flows on in endless song (How can I keep from singing) (CH 565 / MP 1210) and Put all your trust in God (CH 270) would be some classic hymns linking to the Epistle and faith in God through difficult times while Stand, O stand firm (WGRG) from Cameroon or Yet not I but through Christ in me (CCLI) are some options in other styles.
There are lots of good Ascension songs to finish with including rousing classics such as Crown him with many crowns (CH 459 / MP 109), Shine, Jesus, shine (CH 448 / MP 445), At the name of Jesus (CH 458 / MP 41) and All hail the power of jesus’ name (CH 457 / MP 13) while King of kings majesty (MP 1000 / CCLI) starts more gently but is still a powerful closing song. Across the lands (MP 1141 / CCLI / Getty) is one of the less well known Getty/Townend songs but would fit very well, as would the short chant of For yours is the Kingdom (WGRG).