You like so many things about music and you have seen so many cool things played by professionals, but you do not know which instrument to choose for yourself (or your child). This is actually good news!
Here are some things that will help you make a decision:
1. Size. Some instruments these days come in different sizes, like the violin and the guitar, so these instruments will work for ages as young as four 3 years old. Other instruments require that you wait until you are in middle school, like the trumpet.
2. Free Trial Lesson. If there is an instrument that you or your child have some interest in, contact a music academy, a music store or an online teacher (I am available for instance) where they offer lessons to see if you can come in and give an instrument a try (more about this here).
3. Band & Orchestra. For students all the way up through college there is the possibility of taking a class to learn an instrument in the United States of America. One thing that will help you here is to look for the instruments that are few in number because you will get more attention and it will open up opportunities towards learning other instruments as you progress. For example, you may start out with viola in the orchestra, but then make the move towards the violin since they are so similar. Whatever instrument you learn will give you skills to learn other instruments as well.
Parents and students, it is important to remember that whether it's the piano, the cello, or the saxophone, you (and your child) will gain a musical education, some discipline, and it can be enjoyable. I have noticed parents being very concerned when their child does not like a certain instrument. Sometimes students are looking for a certain feeling towards an instrument. Feelings come and go, so if you hold on and keep playing your instrument, over time your affection for the music you play will transcend the up-and-down feelings that all musicians experience.
If the reason you want your child to really like the instrument is because you think that will keep them motivated to practice, let me assure you that the hype of something new is very transitory. It is more important that you and your child value and enjoy the learning experience, that you learn to practice even when the feelings are not there, and find ways to get inspired (more on inspiring to practice here). So, definitely take in consideration that you (or your child) likes the instrument, but remember that we all grow to love things as well.
I admire the approach that some Asian parents take towards music lessons. They see private lessons as a part of the overall education of their children, so viola lessons are next to Math and Science.
I encourage you consider music lessons as building you and your family into a well-rounded people, try a free trial lesson, find a good teacher (more about this here) and give it a year!
More information on picking out an instrument here