When buying a musical instrument - especially your first one, watch out for the following;

1st rule, Too good to be true, is.  An amazingly inexpensive brand new flute or sax or trumpet (or any instrument) will be worse than useless.  It may function poorly or not at all, making playing frustrating and difficult.  A terrible choice for a learner.  You can't learn to play on something that does not work.  It may look great, and appear to work well, when brand new....but not for long.

Don't buy a "no-name" brand instrument, even a brand new one.  Cheap copies are NOT the quality of the instruments they copy.  "Just like a Selmer" is NOT just like one.  Research brands and buy from a respected manufacturer, or risk wasting your money entirely.

When buying a used instrument, possibly a good choice as a quality instrument can be had cheaper than brand new, assume the instrument will require SOME repairs or adjustments, even if the seller says "it looks perfect" or "like brand new".  Unless the seller is a repair shop, they'll have no idea what it might need.  Assume they are NOT an authority on instruments - few are.  Repairs can be very expensive.  See if the seller will have shop check it out for you before you buy, then talk to the shop yourself. "So-and-so told me it just needs a tune up" isn't good enough.  Research the make and model, and it's pros and cons, and it's value, (assuming good condition) before you make a decision.  Instruments that have been sitting around not being played for years could be in very bad shape - just from sitting around.  Ex-rentals tend to have been knocked around sometimes.  Ask about the history of the instrument.  Ask is there evidence of past repairs?  Ask are there obvious defects or damage?  If they won't or can't answer, don't buy.

Just because the ad seems to tell everything about the instrument, remember, it is just the seller's opinion, and they may still know nothing about it.  Anyone can download information from the internet and put that information into an ad.

If you're buying a vintage instrument - again check the make and model for quality - expect that it probably needs major restoration in order to be made functional again, or it could be beyond repair,  unless it says "just restored or overhauled by blank repair shop."  get proof of the overhaul,  such work is expensive.  Again, see if the seller is willing to let a shop look at it before you decide to buy.  Look into the cost of a complete overhaul and factor that cost into your buying decision and the price you'll pay for it.  And all of the other rules about used instruments apply.

Watch out for anything sold "as-is".  Consider that phrase a giant, blinking neon warning sign.  And expect such items to be non-returnable.

And the usual stuff,  pay using a protected method,  be sure of the seller's return policy,  read ALL of the seller's feedback before deciding to buy.