I wanted to respond to Enviroguy, too. He makes some points that should be discussed.
There's two way to look at this. If a music student asks his teacher a question like this, the usual and usually correct answer is to tell the student that what they are playing now is fine and they should concentrate on practice and learn to play better.
The answer is "sometimes".
In the particular instance we're talking about, the teacher is the generic "band director" which generally means "brass player". He may not know that there is much variation in mouthpieces for sax.
But I am a sax player and teacher (former to both) and I could tell the student, "You have a POS mouthpiece. You should replace it with $whatever" OR say "You have fine equipment. You just need to practice more."
In this instance, you have a student with a decent mouthpiece, but is playing on reeds that even his teacher says are too thin. Plus, he's havening questions about his strap and ligature.
The BEST suggestion is, "Get a sax teacher who knows what he's doing and can make a better judgment -- and follow his advice. Failing that, get some stronger reeds, as your instructor says, ans see if your playing improves. Don't worry about the strap or lig unless they're broken/don't fit."
But, for a kid with no teacher, other than what they get in school band class, and no hope of ever getting one, a question like this shows they care enough to want better equipment. If they are like I was as a kid and they have to teach themselves to play, upgrading a mouthpiece might be just the thing to show them more is possible and it may give them the mental edge to become a more serious player in the future.
In this particular instance, I've already said that the student is disagreeing with the instructor on which reeds to use. That's a red flag for me. It's an indication of, "I just have GAS." Studentia don't need GAS. They need antacids.
"Teaching yourself how to play" is something that I don't even want to consider. I will say that playing sax is easy. Playing it well is hard. If you're teaching yourself, you may have a fool for a teacher: no offense, but if you walk up to your teacher with a Mark VI and a Selmer Soloist mouthpiece with Vandoren V12 #3 reeds and he says, "That's all junk. You need to buy something else," you need a different teacher.
Finally, on this point, there is too much emphasis on the "stuff". Can "stuff" make you better? Sometimes, but if you
already have good "stuff" and you're havening problems, buying more "stuff" in hopes of fixing the problem --
especially when you can't even define the problem -- is a waste of money.
And, possibly, you'll make your problems worse.
As a fifteen year-old, my swapping of my stock mpc for the Selmer S80 I found in the old case made me believe I had something better. And that took further than my peers. If we can give a kid that kind of belief (and possibly a little better response and tone), we may have done that kid a great service in the long run.
As mentioned, I had a similar experience, but we were swapping "junk" for "good". The student that inspired this thread already had "good" but had some non-specific problem with it. There was literally no way to be able to define what "better" would be.
You dig, man?