There are many factors that figure into an end product of a good sound on saxophone. Many are player related and many are equipment related. Where do you start when you want to get a better sound?
You can research the exact set-up someone like David Sanborn uses and buy all of it. Problem is, the person on the other end of the sax is not Sanborn, and that set-up might not even work for you. The real question should be, "How do I find my voice on the sax?"
The player and the saxophone make an interesting relationship. We each have physical attributes that impact that end product and the goal needs to be the best possible tone at the end of the day.
Since you have some control over the player side of the equation, the place to start is with you. A good sax teacher can be a great help. The saxophone requires air to play and how you blow, how much air you use, the embouchure you have including how much mouthpiece you take into your mouth and proper placement of lips and teeth have a huge effect on tone. If you have very little mouthpiece in your mouth, the tone will sound more covered and quiet; if you have way too much in your mouth it can be harsh and honky.
If you were going to plan a trip to another city, Google maps requires a starting address and destination. The same process involves being aware of how you sound right now, and developing a goal sound to move towards. This process takes some time, and requires small changes in the direction of the sound you want to emulate. The key words are "process" and "direction". YouTube is an amazing resource for listening to great saxophone sounds. You have to listen a lot and begin developing a sound concept for where you would like to go. Listen to sax players and find goal sounds you love. Make sure you are playing correctly on the gear you have and getting the most you can out of it first.
Once you have a start and end destination in your mind, you are ready to try some equipment related options. The easiest and cheapest place to start is with reeds. The reed and then mouthpiece are the 2 biggest products that affect your sound. Reeds come in all shapes and sizes. A jazz reed or classical reed will add or reduce brightness. The strength of the reed will do the same; hard reeds = louder, better high end; soft reeds = softer, easier low end.
Many young jazz students will find a Rico Plasticover reed will get them the volume they needed for jazz band and a bigger overall, or brighter sound. Sometimes the quick fix will just be a reed purchase. Once you have the best sound you can get on your existing set up, you then can listen some more and see if you are closer to that goal sound and decide if a mouthpiece is the next step. I always advise a few months of adjustment time between any equipment changes. If you change to new reeds, play them for a while before trying mouthpieces. This is a process!
If the reed takes you in the right direction – What mouthpiece do you then try? I always advise young players to go with the safe options. As the player gets more advanced, they can try more individual options because they will be ready to know if that new mouthpiece is really worth the cost.
Safe alto mouthpieces would be Selmer or Rousseau for traditional music and Meyer or Rousseau Jazz hard rubber, or Yanagisawa, Beechler or Dukoff metal for jazz playing. Tenor jazz pieces might be an Otto Link or Yanagisawa metal, and Selmer or Rousseau for traditional styles.
The process is to take one thing at a time and move in the direction of the goal of your desired sound. Good luck!