You have thought about private lessons for you or your child, you have found a teacher, but you do not have an instrument. So what should you do? Buy or rent, that is the question. Some parents are not sure if it is worth buying an instrument when they are not sure how long they or their child will be playing.
Here is the quick answer: buy the instrument.
Why? Because in the end it is cheaper, at least for violin, viola, and cello. How so? Because the money you pay for renting the instrument is lost, the money invested in buying an instrument can be won back if the instrument is kept in decent shape. The only hardship that you have in buying the instrument is selling it. But that is not a problem, because there are plenty of people looking for instruments, you can even sell it at a music store. In the end, you win out if you buy the instrument.
It may be different for brass, woodwind, or percussion instruments, so you may need to ask questions of different sellers. It takes a little work, but you can save more money than you think.