The saxophone, mouthpiece, reed, etc do make a difference in your sound.
Playing on a broken sax is difficult and frustrating.
Using the wrong combination of mouthpiece/reed can also make things harder than they need to be.
The mouthpiece/reed actually make more difference in your sound than the saxophone itself most times (as long as the saxophone is not in horrible shape).
Currently I’m using a Vandoren V16 (mine is a T9) on tenor sax and a V16 A8 on alto sax. If you need to play softly, for something like classical music, you want a more closed tip opening. If you want more volume/edge, you might want a wider tip opening. A tip opening of 6 or 7 might be a good midrange number. Some sax players will want a more closed mouthpiece, others will want one that’s more open.
The tenor piece was given to me by George Young after I tried a few different sizes. The number after the letter stands for the width of the tip opening.
There are a few other variations associated with mouthpieces including baffle and chamber size.
I have not played around too much with those. I have mostly played on medium chamber pieces and I haven’t messed around with baffles.
Before the V16 mouthpiece, I used both a Selmer Metal piece 7* on tenor and a Meyer 8.
Metal pieces will be brighter, which works well in some styles of music when you want to cut through. It also has less bottom in the harmonics so the sound isn’t as full.
The hard rubber V16 seems to be working well for me as a pretty versatile mouthpiece that gets some volume.
The reeds I use with it are Vandoren V16’s size 2. That lower number reed means it’s a softer reed, which corresponds with the higher number on my mouthpiece. Generally if you have a higher number on your mouthpiece tip opening, you want a lower number reed and vice versa.
Here are a few more posts on saxophone equipment:
New Sax Mouthpiece? How to Adjust Your Setup
Beginning Sax – Reed and Mouthpiece Issues!
My Return From the Darkside of Synthetic Saxophone Reeds
Lenny Pickett Mouthpiece – What’s He Playing?
Saxophone Brands