You will need your own instrument, bow, rosin, and cleaning cloth. If you don't already own an instrument I will gladly walk you through your first purchase. It is always wise to consult your teacher BEFORE purchasing an instrument as not all instruments are created equal and instruments come in various sizes to match the player.
The sheet music you will need will depend on your experience level and your musical aspirations. I also recommend a set of color pencils and mechanical pencils with good erasers. Musicians do not write on music with ink.
If you are comfortable with technology we can skip the sheet music and use SmartMusic as a replacement for most method books.
Additional Instrument Supplies
Those studying violin and viola will need a shoulder rest. For younger beginners I recommend a simple foam sponge, more advanced students need a proper shoulder rest to support their instrument.
Those studying cello and bass you will need some kind of rock stop to hold your instrument up. I recommend a strap rock stop that will attach to a chair or stool. Cellists will need a chair appropriate to your height, adjustable stools work perfectly for young cellists.
Tech Supplies if you choose online lessons
You do not need an advanced set up to take virtual lessons. A smartphone or tablet will work. For a better experience, a laptop with an HD webcam can help me see fine details in playing. I also recommend an inexpensive USB microphone. I use a Yeti Snowball that retails for $50 and it works quite well.