My children love music.
I've never been the kind of mom that pushes them into five million things to constantly keep them, and me, busy. I've been a "Hey, you're interested in that? Well why don't we try it out for awhile and see how it goes," kind of mom. And when they lose interest (after talking things over first, of course) I back off and let them find something different, and in the meantime do what I can to encourage without being pushy, to keep their level of excitement high, and to get the family involved for moral support.
With me being a piano teacher, music is a fixture in our home and the older children learned early to enjoy good music and to see how enjoyable it is (except when I'm having a hard time mastering a piece and take my frustration out on the poor piano). My oldest wanted to learn piano when she was about five. I let her goof around on the piano as much as she wanted, but as a teacher I generally don't encourage beginning children too early--their ability can quickly outstrip their physical readiness if you do. But when she turned eight--or nearly eight--I started teaching her.
She didn't like it so well. Neither did I.
My son later took a turn at the piano with similar results.
He also took a turn at baseball for a couple of seasons.
After that it was the violin for my oldest daughter. She had a chance to take some introductory lessons through her school and fell in love with the strings. In middle school she switched to viola and fell even more deeply in love with the richer tones and mellower sound of that instrument. Once she proved herself dedicated we purchased an inexpensive beginning instrument and got her going on lessons.
*A word to the wise at this point--when it comes to instruments, for the most part, you get what you pay for. Our inexpensive instrument became considerably more expensive after a couple hundred dollars worth of adjustments to make it playable. Also find a good teacher who you can actually work with. Her first was awful.*
Then my son took up the clarinet and the bagpipes. We bought him a good used clarinet at a pawn shop and a bagpipe chanter on ebay. No bagpipes yet. We'll get to those in a couple of years hopefully, expecting to pay upwards of $1000 for a good set.
Now my son has become interested in the tenor sax so he can play with the school's jazz band. Has he given up the other instruments? Nope. He wouldn't dare be so easy on us. With him we can get by with 2 teachers as the clarinet and tenor sax are almost identical in fingering. BUT that means he could use a tenor sax. The one he currently has is a rental with option to buy. We just may end up doing that. The disadvantage to rent-to-own is that you end up paying more for the instrument than it's worth. The advantage is that it's still owned by the shop, so maintenance is free until it's paid off.
Now my youngest, of course, wants to follow suit. She wants to play guitar and mandolin. Fortunately I can get a pretty good guitar for under $200. A mandolin is another matter entirely, but the fingering is pretty much the same as on a guitar, so she learns one she can learn them both.
On top of all that my kids are interested in other minor instruments as well, and all three are (again) taking piano lessons.
So, in my house right now we have:
1 tenor saxophone
1 bagpipe chanter
2 penny whistles
1 bodhran (Celtic drum)
1 lap harp
AND my daughter wants to buy an electric violin. I'm all for it. She can plug the dang thing into headphones and play for ears only.**
**NOTE: She's actually very good, but the noise level at my house, as you might imagine, can sometimes drive one to distraction.