You can find a YouTube playlist here with many of the songs suggested below.
There are themes throughout today’s readings exploring inclusivity and who is welcome in the house of God so you could begin by offering everyone an open invitation to join in worship together with a great range of well-known contemporary hymns you could use including Here in this place / Gather us in (CH 623), Let us build a house (CH 198), For everyone born a place at the table (CH 685) and Jesus calls us here to meet him (CH 510). One church, one voice (Satellite) and All are welcome (OCP) would both be great for bands and have easy but catchy choruses which congregations should pick up quickly, the latter being a great alternative to “Let us build a house”.
There are very few options for singing Psalm 15 with Lord, who may dwell within your house (Jubilate) probably the best metrical setting in contemporary language, although the meter gives a limited selection of tunes. The Scottish Psalter is always a good fallback for finding a metrical setting in these situations so Within thy tabernacle, Lord (Hymnary) is an option if you’re comfortable with older language. Lord, who may enter your house? (CH 8) is a good responsorial option with a simple chorus while if the chant style of the verses is unfamiliar then the words could also be spoken over the same chord sequence.
The Beatitudes have inspired many songwriters but the main challenge is finding songs that can be sung by a congregation. Blessed are you (GIA) is one of most accessible metrical options with a new tune while Blessed are the poor in spirit (Carolyn) would suit those looking to sing a familiar tune. There are two songs by John Bell and Graham Maule that are very easy as both feature a chorus while a soloist or choir could sing the verses, Hey my love (WGRG) and Amen, amen, it shall be so (WGRG), while another short chant you could consider is Beati voi poveri (Taizé). You have shown us (CCLI), Blessed are the humble (CCLI / Kendrick) or Blessed (link) would suit bands while for something completely different there is also a Greek Orthodox setting of The Beatitudes (link) in English.
It’s also important to add a note here that the most widely published setting of the Beatitudes (Blest are they, the poor in spirit) is written by the composer David Haas who has faced numerous allegations of sexual misconduct and many publishers and churches in North America having stopped publishing or singing his songs as a result in order to stand with victims. For those wishing to explore some of the complexities around this, the statement by the Mennonite Worship and Song Committee from June 2020 (link) is a helpful starting point.
Take up your cross (CH 402 / MP 935) would work well as a personal response to the Epistle as it picks up the themes of weakness and foolishness. There are many other songs about the cross which you could use but The power of the cross (MP 1217 / CCLI / Getty) and In the cross of Christ I glory (CH 397 / MP 338) are perhaps the most relevant for this passage.
The Old Testament gives us another hugely popular passage which has been set in various musical styles. If you want to sing Micah 6:8 then options include Act justly (OCP) which would suit piano or organ, the worship song Act justly, love mercy, walk humbly (CCLI), or my own Act justly (link p237) which is fun to sing in three parts and can be done with band, just with percussion or entirely a cappella. You could also look at songs which link with the wider themes of the reading such as Heaven shall not wait (CH 362), For the world and all its people (CH 262) and When the hungry who have nothing (CH 258).
The Old Testament message about what God requires of us is a good sending theme which can link to songs about action and justice such as Forth in thy name, O Lord, I go (CH 529 / MP 159), May the God of hope go with us every day (CH 256), Canticle of the turning (Wild Goose / PFAS 75B / MV 120), God of all comfort (Resound) and El mensaje que hoy proclamamos / Hear the message we now are proclaiming (H 46). Lord, for the years (CH 159 / MP 428) and God loved the world so much (WGRG) would also link to the Epistle.