Where To Find Scriptures To Use For Contemplation

David,
Good questions on where to look for passages to contemplate.
It has long been the monastic tradition to focus primarily (but not exclusively) on the Psalms and the four Gospels.
It is a good practice to have some sort of regular “diet” of these biblical books anyway. Then you might run across a passage that seems to present itself to you. At the time, you may just want to note it. Then, later, you can go to it with the steps of contemplation in mind.
It has helped me to try to stay current with the prayers in the Liturgy of the Hours. I started praying these as a Protestant, and I have found nothing else that has so helped me in adding the right touch of structure to get my prayer life out of a muttering neutral. The Liturgy of the Hours, also known as Christian Prayer, or the Divine Office, places before you many of the Psalms, other Old Testament and New Testament canticles, and readings from the New Testament letters. I highly recommend this prayer form to any Christian. I have given away or referred Christian Prayer to several Protestant friends, and they have all been deeply grateful for the introduction. It is one of my Top 10 great books for the inner life.
Gil Sanchez, my sponsor when I became Catholic, introduced me to it, and he, in turn, was advised to look into it by his spiritual director, a monk at Holy Trinity Abbey.
Or, you may want to read through the Psalms and underline or take note of four or five lines that you would like to use for the purposes of contemplation.
Liturgical churches also have daily readings, and these can be used to source your contemplative needs.
Let me say this – you won’t need 365 of these per year. It is my experience that some contemplative words or phrases become active in the heart for many days before I feel ready to move on. One doesn’t really move on until one is convinced that God is ready to take you elsewhere.