38 views and no replies. Hmmm . . . maybe there isn't an answer to your question, except for us to go through the same mouthpiece recommendations that everyone makes to the myriad of similar questions asked on SOTW about the same thing.
First of all, what is a "125" model? I know Selmer adds some additional numbers to their models (but rarely uses those numbers except in catalogs) and few of us can follow the continuing onslaught of model designators. To me, a Serie III is sufficient for me to know generally what you have. Did a mouthpiece come with it? If you bought it new, I'm assuming it did. What was it?
What are you using on it now? And, what are you missing on your current set-up or the supplied mouthpiece (which are usually decent pieces from Selmer) that you think you could improve upon?
In my experience, the Serie III is a VERY bright alto, much more so than the Serie II and especially the Ref 54. So, you may want to look at mouthpieces that will take some edge and brightness off your alto. But that is a very personal decision and one that only you can make.
As far as classic music as opposed to jazz, I don't believe it matters, but others will probably disagree. I'm one to think that once you choose a mouthpiece/reed combination that you like (and is in tune with little need for control), then you can push any kind of music you want to push through it. Good tone is good tone regardless of whether you are playing jazz or classical or swing or R&B, etc.
So there's a start . . . DAVE