When I meet a mouthpiece customer for a fitting session, there are 5 primary questions that I ask him or her. The answers to these questions have a direct effect on what we will explore in terms of a different mouthpiece.
Classical music uses a lower baffle and a large chamber and therefore slower air.
Mainstream Jazz uses a higher baffle and a smaller chamber and therefore faster air. Below are some traditional marriages of the last 40 years for horns and mouthpieces. Don't use a reed that you have played on your old mouthpiece. This is because it is warped to the contours of your old mouthpiece and will not perform well on the new one unless it is exactly the same, which is an impossibility. Have your old mouthpiece with a good reed with you to use as a reference point.