Cushioned neck strap, preferably Neotech brand
Make sure it is for the correct type of saxophone (i.e. if you play alto saxophone, you should have an alto saxophone neck strap; if you play tenor saxophone, you should have a tenor saxophone neck strap).
Reeds (Read more about reeds here.)
We recommend #2 strength Rico reeds for beginners.
We recommend #2.5 strength Rico or Rico Royal reeds for second-year players.
It is best to buy a box of 5 or 10 so you have extras when they are no longer usable (after about 2-3 weeks of playing, or when they get chipped).
Cork grease:
One stick is typically enough for a whole school year.
Cleaning swab:
Make sure it has a weighted string to help you pull it through the instrument.
A silk swab is best, but felt or cotton will work too.
Mouthpiece Saver
Strongly recommend, but not required
This is a piece of rubber or plastic that sticks to the top of the mouthpiece, guarding it from teeth marks.
These usually cost $1-$2.
Mouthpiece and Ligature:
These typically come with the instrument already.
Check with your teacher if you need to purchase a new mouthpiece or ligature for recommendations of brands.
Make sure the ligature is the correct size for your mouthpiece before purchasing.