Musical instruction provides many benefits. It is great to see the sense of accomplishment on the face of a child as they play a song they love on an instrument for friends and family. They learn discipline, and that working hard produces results. There is so much more they gain, that it is hard to express. There is even research that suggests that music makes children smarter, and better at math.
Overall - it is fun!
I am not going to presume to tell you which instrument your students should learn - although I will tell you my plan.
Although Charlotte Mason did not generally advocate set lessons (in any subject) for children under the age of 6, I feel that the thoughts of some educators that came after her can be looked at. Please see my post on this topic. In this case, I feel that the work of Dr. Suzuki and his work with teaching young children to play the violin should not be ignored.
I feel that Suzuki music lessons on an instrument provide so much for children. My sister was a young Suzuki violin student starting in 1965, and although she does not regularly play violin, she can when she wants to. She also easily learned other musical instruments that interested her. I personally took Yamaha Organ Lessons (a somewhat similar program) starting at age 3, and I also learn instruments fast. We were also both gifted in math.... if it really is related.
At the least in Year 0, you should provide much quality music for your child to hear. This does not have to be a sit-down affair, but may be played in the background as they go to sleep, as they play, or in the car. My 3 year old daughter, Echo, regularly puts on a Suzuki violin CD by herself as she plays. I also recommend starting Suzuki lessons. If your child seems drawn to an instrument, see if there is a Suzuki instructor. (Note - make sure it is a Suzuki certified instructor if you are paying for Suzuki lessons! Many teachers use the books, without using the methods.)
In Year 0 or higher, I recommend learning some type of instrument. This may seem daunting if you are not musical yourself. If you find a good teacher, this will be quite easy. This is also my recommendation. However, if this is not feasible, there are other options. This blog has a good article on teaching anything (including music) when you don't already know it. Keep in mind that instruction by a person who is not qualified to be a teacher can end up limiting the student in that instrument. This happened to Dr. Suzuki himself, as well as many other people. If the student later goes to a teacher, the teacher and student may be frustrated while fixing bad habits in technique. However, it can be satisfactory within those limits - and this method will be used in my own homeschool.
If Money is Tight, (as it often is) - don't give up the hope of playing instruments! Music programs from places like Universities, Music Conservatories, or associated with symphonies may provide bursaries to students that need the assistance. Bursaries will not pay the entire cost, but can make a huge difference. Another option is mentioned above - learning ahead and teaching yourself. If you don't have any instruments, buy an inexpensive recorder (they have them at the dollar store here!), and download the first few lessons from the Nine Note Recorder website! If it goes well, the course is very inexpensive to buy. Recorder can be beautiful, and the site has many resources.
Our Homeschool Plan
Throughout - provide a variety of instruments. We have over the last few years bought or made cymbals, maracas, child-sized guitars (inexpensive), a xylophone, can drums and more.
Suzuki Violin. - taught by Suzuki teacher
Suzuki Violin - taught by Suzuki teacher
Piano - "My First Piano Adventures" - taught by me. (I play some piano...)
continue with Violin and Piano - provide opportunities for self-teaching other instruments as can be afforded and as interest exists. (ie, recorder, guitar.) These other instruments would be only as the student is interested.
Remember, your choice of instruments and programs is up to you.... but do something, even if only an inexpensive instrument like a recorder or harmonica!