At such a young age, it is not always the best idea to buy an instrument or long-term item. However, once a student is fully grown and feels that they wish to play for many years to come, buying an instrument, case, etc. may seem the most cost-effective option. Before buying, it is important to always talk to your school teacher (myself) and your private teacher (if you have one) in order to receive good advice on where and how to shop responsibly. You NEVER want to shop for an instrument online, unless you know the dealer well. In person shopping is the best way to get the best investment.
Prior research into what you are looking for is imperative. Shar.com has put together a great online playlist that includes advice on buying instruments (old vs. new), bows, cases, etc. and how to properly take care of them, now that you are the sole owner. Please click here to view the playlist. Also, think about a budget you want to set yourself. For a beginning instrument, you are looking at $1,000 to $5,000, depending on the type of instrument (ex. violin, viola, cello, bass) and whether or not the student wishes to pursue music at the collegiate level. There is never a need to go above $5,000 for your first instrument.
When choosing shops, look at the reviews and policy on buying. Independent and/or family shops are usually the best route to go, as they will spend time with you choosing the right instrument that fits your budget. Do not feel pressured to buy an instrument from the first shop you go to. You may want to go to 2 or 3 shops before deciding to buy. When trying instruments, it is best to ask the shop to provide instruments in a certain price range (ex. $1,000 to $2,500). Then, try out the instrument without looking at the tag. Sometimes you will much prefer the sound of a cheaper instrument to a more expensive one!
Lastly, talk to your insurance company about making a policy for your instrument. You do not want to be out a couple grand if your instrument is lost in an accident.