You can find a YouTube playlist here with many of the songs suggested below.
In Matthew we find an invitation from Jesus "Come to me, all you that are weary and are carrying heavy burdens, and I will give you rest". This could naturally link to songs such as I heard the voice of Jesus say (CH 540 / MP 275), Come and find the quiet centre (CH 716) or When the storms are overwhelming (Resound). A more general option would be a song which speaks of trust in God who is there for us at all times and classic hymns which fit well are What a friend we have in Jesus (CH 547 / MP 746) and Praise, my soul, the King of heaven (CH 160 / MP 560) while Build my life (CCLI) and Way Maker (CCLI) are more recent options.
The text from Romans also offers an opportunity to tailor your time of confession and some sung responses to this could be Create in me a clean heart (PFAS 51F), which resonates with the focus on the struggle within our body, or Jesus Christ - Perfect Love (STF 325 / CCLI).
Psalm 45 is not one which many writers have set and this is a psalm very much in two parts so if you are following the lectionary it seems important to focus on the second half or else you shift the emphasis from addressing a woman to addressing a man. The 1929 Scottish Psalter offers us O daughter, take good heed (Hymnary - omit refrain) to the tune St Michael while for a more contemporary setting, Wake up, O daughter of Zion (Kimbrough) is a beautiful song which brings this text together with Isaiah chapters 52 and 62.
Many contemporary songwriters have been inspired by the passage from Matthew to write quite reflective songs including Come to me (CH 759), Come to me (Kimbrough), Come, come, come (Gordon), Come bring your burdens to God (WGRG) and Come and find rest in Christ (WGRG) while you could also use some of the options suggested under the Gathering section. With the reflective theme, this would be a great opportunity to learn a new song introduced initially by a solo voice or small group of singers and you could also consider using some of the shorter songs as sung prayer responses.
I need thee every hour (CH 556 / MP 288) and It is well with my soul (CCLI) would be two well known options to respond to the Epistle and you could also consider Thou hidden love of God (CH 188), the fourth century hymn Lord Jesus, think on me (CH 491), and Just as I am (CH 553 / MP 396). With the latter make sure that you check which tune your congregation know as the opening of Saffron Walden and Misericordia are very similar and you can easily sing the wrong one without realising it.
Genesis is a more challenging text to offer suggestions on without knowing the exact focus of a sermon, but a song such as Your love, O God, has called us here (CH 695) which speaks of the love between a couple and the love of God might work.
Like with gathering songs, you might want to finish with songs about trust in God and God's faithfulness. There are lots of well known options across a range of styles including Be thou my vision (CH 465 / MP 51), Great is thy faithfulness (CH 153 / MP 200), Cornerstone (CCLI / YouTube), and In Christ alone (MP 1072 / Getty / CCLI). If you have focused on Romans then you could also consider songs which focus more on overcoming sin such as And can it be (CH 396 / MP 33), and O Jesus, I have promised (CH 644 / MP 501).