With the caveat that I am in my 60s, which means that children back in my day had very little options other than obeying their parents…
…I was very blessed, unbelievably so, to have a piano teacher who was the church music minister in her large Lutheran church. She was classically trained and had a degree in “Music,” not “Liturgical Music” or “Music Ministry.” But her focus in life was “liturgical music and music ministry.”
Before recitals, she would call all her students into a circle and we would pray that God would receive the glory for what we played.
And from the first year I studied with her (I was with her for 10 years until I graduated from high school), she got me involved with playing in churches. I had my first paying job at a little church–$5.00/week, which was big bucks back then! But even more important than the five-spot was the EXPERIENCE I gained week after week playing for a very friendly and appreciative congregation.
When I started taking organ lessons as an adult, I had (and currently still use) a teacher who is a church music minister in a liturgical church (Episcopal) and has much the same love for hymns that I have.
I would strongly suggest that Catholics who are considering involving their children or themselves in music lessons seek out a teacher who emphasizes glorifying God and serving in church with their music. I think it’s more likely that the children will stick with it if they have a reason for practicing and having lessons. A lot of children quit music lessons because that phase of their life (high school,) ends and they move on to other pursuits (job, military, futher education, marriage, etc.). But if they are “church-trained,” that part of their life, hopefully, will never end and their music will continue to be relevant and very-much needed.
I hope parents are reading this. We are so short of musicians in parishes.