When looking for a new mouthpiece I think it is a great idea to try out a few mouthpieces before you decide on making the purchase. I have some recommendations for classical mouthpieces. These mouthpieces will suit playing in a concert band or solo setting.
For the saxophone (soprano, alto, tenor, bari) I recommend trying out the Selmer S-90, Vandoren Optimum, and the Eugene Rousseau NC (new classic). These three mouthpieces are good options to try out when looking to upgrade your mouthpieces. They all will help you achieve a warm, smooth, and consistent sound that is needed for concert band and solo playing.
For the Clarinet I recommend trying out the Vandoren B45, M15/M30. Most mouthpieces from vandoren play amazing for the clarinet. I recommend these specific models, because they are a great option for your first upgrade mouthpiece. They will help achieve a more clear tone on the clarinet without changing too much from what you were previously used to. There are other options worth trying from the D’addario line, but I believe that the Vandoren line is a great place to start!