My dd has sung in our local church choir since we moved here (she was just 6). She also sings in two school choirs.
Learning an instrument or singing - making music in other words - actually does make permanent changes in the brain. There will more connections between individual neurons. The effect is similar to learning another language. Practically, these brain changes affect positively the way the brain analyses things, solves problems, and many other functions.
Listening to particular types of music will enhance your thinking skills - Mozart has been used as an example of music which does that, but also Bach (there are plenty of others but I'm not listening to Mozart atm and my thinking/memory skills are opertaing distinctly under par!).
I knew a family whose 6 month old dd was given a violin. Every day one of the parents put that violin under her chin and held her hand at its neck! Now, I don't necessarily advocate that, but I do think that you can start whenever you like. If a child is interested in a particular instrument then they're old enough to start learning to play it. Learning to read music while very young is much easier than learning to read music later in life. One family of my relatives all started learning violin (their father's instrument) when they were only about 2! I used to watch those tiny children running to get the tiny little violin when they were to have a lesson! They loved it. As adults they all play beautifully. There is so much delight and companionship involved in playing. I believe that recently research found that singing made you happy! What better reason to do it! DD and I have both always used singing as a way to cheer ourselves up, without actually realizing it!
We are quite lucky in my town. There is a small 'gang' of people who organize concerts periodically. They know a lot of classical musicians, and somehow or other persuade them to come and give recitals in the church every couple of months. DD loves them, she sells tickets on the door, helps 'backstage', looks after volatile artistes, you name it!
About 4 years ago I took dd to see a local performance of Marriage of Figaro. She was entranced. We try to go whenever it's on (finances permitting), either here or in London. I have played her recordings of Cosi fan Tutti, which she likes but not so much; Bach, . Mahler and Wagner are not to her taste, but she is only 12 and her dad loathes opera with a vengeance (and most classical music 
) and he will tell her loudly how vile it is. (I'm afraid I used to use Das Lieder Von der Erde to get rid of visitors who wouldn't leave. I would play it over and over and insist that they listen rather than talk, point out particularly interesting phrases - I'd make it all up! - until they left.my excuse is I was pretty young and some men are horribly persistent.)
DD loves The Sixteen. Caldara Crucifixus is her favorite, and one of her ambitions is to perform it. I think it's what the angels sing in heaven. She liked Rossini Petite Messe Solenelle too, and lieder - Die Lorelei has a special place in both our hearts. Like me, she prefers music which involves singing.
DD is not solely a classical fan. She sings a lot folk, sometimes accompanied by dh on guitar. Dylan, the Stones, Evanescence, Glenn Miller, Alison Krauss. Her tastes are catholic.
Music is everywhere. We can hear it when we go into a shop, but classical music is not so easy to get unless someone in your family loves it. I think children shoulto hear classical music at school too. So many primary school choirs sing Abba and the like. That's fine, but classical music will challenge them more and expands their minds, stretches their brains and fires imagination. There are so many wonderful pieces which children can easily follow and enjoy. Britten's arrangements of folk songs, Peter and the Wolf, Purcell Come Ye Sons of Art. All these can be played at nursery, in Reception.
I believe that being involved in classical music expands horizons, broadens knowledge and experience, facilitates depth of thought, enhances imagination and encourages concentration.