Re: Cannonball saxophones.
That sounds like a good plan. What are you using now? What do you like about it? What do you wish was different? My general recommendation for players wishing to develop their own jazz sound is to go with large-chambered pieces with small baffles and a medium-to-medium-large tip size. The best known pieces in that category are the Otto Link pieces, but there are other good mouthpieces based on that same general design. I play Links, but I hand-corrected some defects on them to improve their response. Machine-finished pieces such as the Links are notorious for being inconsistent. The Van Doren V-16 gets good press. Saxgourmet sells a piece called the Blues Blaster that I find intriguing because it is similar to a Link Super Tone Master and is a hand-finished piece that goes for about the same price as the STM. So either the V-16 or the Blues Blaster might have a critical quality edge over what Otto Link offers. Other mouthpiece designs with smaller chambers and larger baffles are good for specific purposes - greater projection, volume, and brightness - but they mold your sound more.
One key advantage to doing the mouthpiece first is that you can budget for the mouthpiece that suits you best without being limited by what you just spent on a horn, and a mouthpiece ranks higher than the horn in terms of your sound. Also, testing horns with the mouthpiece you want to use will eliminate the unpleasant surprises, such as intonation problems, that you might find if you change a mouthpiece for some reason after you've gotten the new horn.
There are several brands of good quality, moderately priced Asian horns that can be found in better music stores, including Cannonball, Antigua, RS Berkeley, and Paul Mauriat. They all offer a variety of finishes. You can find dealers on the websites for those brands. Good luck and good hunting!