Last year I bought a new Yanagisawa A-WO1 from Europe for $2100. I don't know if deals like that are still around but you can always look. As opposed to most brands, including Yamaha and Selmer-Paris (and I write this with experience - 60 years of playing), Yanagisawa is one of the few brands that will play great right out of the box without dealer-prep. I won't bore you with the details, suffice to say - I've had experience - and lots of it.
Just this morning I am playing my Yany A-WO1 next to my Selmer-Paris Ref 54 that I bought new several years ago. Both are superb instruments (better than the many Yamahas I've tried - and owned) and if you were so inclined, and willing to risk it, you could probably buy a new Yany for under $3000 (assuming pricing is about the same - but not in the USA - here the new Yanagisawas were going for over $3K the last time I looked). Used Yanys are another good bet - can't tell you the expected pricing (you can find that yourself) but any of the older Yanagisawa models (like A901, A991, A-880, etc.) would likely be more pleasing than a Yamaha or CB.
So, for vintage (say mid 1920's up to say 1954 or so), many of the trusted brands are Buescher, Conn, and Martin.
There are a few web-sites that sell vintage saxophones - mostly already shop-checked and maybe with overhauls. One is vintagesax.com - Gayle Fredenburgh in Florida. Other stores are easy enough to find - USAHorn in New Jersey, Kessler in Las Vegas (a site sponsor), junkdude, etc.
Here on the site are Bruce Bailey, JAYEPDX, saxcop, etc. However, you don't yet qualify for buy/sell here on SOTW. You can look up those rules.
In MY view, one Cannonball model that impressed me was the Vintage (and maybe with the added "Reborn" in the model name) - I played a prototype at NAMM a few years ago that was terrific. The other CB's, not so much, but then everyone has their own prejudices about saxophones. Yamahas? Never played one I liked enough to buy and keep but then again, others love 'em. Again, a personal choice.
I think Yanagisawa and Selmer-Paris are making the best saxophones in the world - these days. DAVE