As the main themes of the Feast of Trumpets are remembrance, and the sounding of the shofar it would be very appropriate to study each on this day. You could do a word study of all of the things YHWH or Yahusha say to remember. I did this as I was gathering this reading list and I would definitely recommend that. You could totally do some art journaling or another activity based on these verses too. Taking a look at where we see shofars and what they stand for throughout Scripture is also time well spent. Of course, a special emphasis on repentance is fitting for all the feast days and we would do well to brush up on a few verses about that.
Prophetically it is believed that the Messiah will return on Trumpets, which would be another great study topic! The return of the Messiah and the start of his reign here on earth. Many verses mention his return and the sounding of shofars together so we can easily see the connection to the Feast of Trumpets.
Here are a few of my favorites to read during this time.
Scriptures to Read During the Feast of Trumpets:
Leviticus 23:23-25 - instruction for this holiday.
Numbers 29:1-6 - instructions for offerings on this day.
Genesis 21:1-13 - a traditional passage to read.
Genesis 22 - the sounding of the shofar is connected with the ram being sacrificed instead of Isaac.
1 Samuel 1-2:10 - it is traditionally believed that Hannah conceived during Yom Teruah.
Jeremiah 31 - Trumpets is described as a day of remembering and this passage is about YHWH remembering his people.
Psalm 98:6 - with shofars shout joyfully before YHWH.
John 15-16:4 - the Messiah instructs us to remember these words.
1 Corinthians 15:51-52 - this significant event could be happening during a future Feast of Trumpets.
1 Thessalonians 4:15-17 - The Messiah will return during a blast of the shofar.
Revelation 8-11 - the seven shofar blasts.
More on the Feast of Trumpets:
The Beginner's Guide to the Feast of Trumpets
The Meaning of Yom Teruah
The Significance of the Shofar During Trumpets