I understand this thought process completely. The trouble in this case is there is no “that” choice available for $1500. If your budget was double you would have received very different answers to your question. $1500 is a decent budget for a “starter” horn.I'm actually hesitant to say that. No matter the instrument people usually have canned answers if you tell them you're a beginner. They always say "start with this then buy that", I'd rather just skip this and buy that. "This" is a waste of money. With all respect, I'm going to go ahead and ask it... What about a sax for beginners could be so important that you don't want to miss? The fingerings are standardized, the action is probably higher (I'm guessing), the mouthpiece seems like it would be of more concern for a beginner, yes? Help me understand.
Going back to the tonal question, for a beginner what is needed is a horn that is in good mechanical condition. All the pads seal, no wiggly keys, action is even and smooth. There will be no perceptible difference to either the player or listener between instruments that meet that standard. There may be an intangible something that makes one horn “click” with you more than another, but tone will be a result of you + mouthpiece and maybe reed.
At $3K and above, you might be able to notice a difference even as a beginner, but $1500 will only buy you a good new student instrument, a good used intermediate-level horn or a decent used 2nd line horn from many decades ago. Note there is really very little difference between student and intermediate level horns. It’s usually just build quality (real pearls, better pads, fit and finish etc.) and maybe accessories that make the difference.
