Instrument - Rent or buy it from a local music store.
DON'T BUY INSTRUMENTS FROM AMAZON, EBAY, WALMART, COSTCO, ETC - THEY ARE TERRIBLE!
Mouthpiece: Yamaha 4C Alto Saxophone Mouthpiece or Premiere by Hite mouthpiece. I highly recommend upgrading to one of these mouthpieces! It makes a HUGE difference!
Mouthpiece Cushion: Vandoren or Rico. A local music store will have something similar. The specific brand isn't crucial here.
Ligature: The ligature that comes with your saxophone will be fine. If you want to upgrade or need another one, I would recommend:
If you have the Yamaha 4C Mouthpiece, I recommend the Yamaha Alto Sax Ligature
If you have the Premiere by Hite Mouthpiece, I recommend the Rovner Alto Sax Ligature
Music stand - to use at home for daily practice. Don't get the cheap, flimsy folding metal music stands - they are garbage. Here are a few suggestions - music stand 1, music stand 2, music stand 3. Your local music store will also have similar options.
Saxophone care kit: Conn Saxophone Care Kit. A local music store will have something similar.
Extra Reeds: Rico reeds (#2 strength) or Vandoren reeds (#1.5 strength). I recommend buying 2 or 3 boxes.
Neck Strap: Neotech Sax Strap Junior (this is an optional upgrade if needed - most saxes will come with a neck strap, but will usually be not as comfortable as this one). A local music store will likely have other options like this. It's nice to have a little more padding.