Some instrument accessories are necessary for every instrument.  For example, reeds for Clarinets and Saxophones are needed in order to make a sound on those instruments, and oil is needed to lubricate brass valves.

There are also other accessories that you may find help you as a musician be more comfortable on your instrument, get a better sound, or make practicing easier.  

Below you can find links to the required accessories for your instrument and links to accessories that I recommend for each instrument but are not required.

I usually recommend parents rent an instrument rather than buying at least for the first few years.  The main reason being, students change their minds about if or what they want to play.

Perhaps more importantly, there are predatory brands on the internet that take advantage of uninformed consumers and sell terrible instruments at very cheap prices.  They will look like quality instruments online but will often be tuned improperly or made so cheaply that when they inevitably break, repair shops refuse to fix them because they know it will continue to break, and ultimately they become totalled.

Please avoid brands like Mendini, Kaizer, Allora, and Jean Paul at all costs.  They may be cheap, but they are also infamously out of tune, made with poor craftsmanship and materials, break constantly, and will not set your child up for success.  They will cost you more money and time in the long run than if you were to rent.

That being said, I am happy to help you find a quality instrument to purchase if you are determined to buy.  Bellow you can find a list of beginner brands/models that can be trusted and I highly recommend.