It sounds to me, and I could be wrong (often am) that this may be a case of listening to someone else...perhaps a recording even & wanting to sound like that and thinking that a different mouthpiece might do the trick. Well, first of all different mouthpieces are going to work differrently for each person. You can read on sax forums how this piece & that piece are so great, maybe so, for that particular person, but that may not be the case for you. Selmer C*'s are probably one of the best all around beginner mouthpieces there are; alot of experienced players still use them & sound really good on them. Forgive the old cliche, but chops don't come in a box, it takes lots of practice & playing to develope a good sound on a sax. You can change the sound of your C* with different reeds...as in LaVoz for a brighter sound, Hemke's for a darker more classical sound & Rico's for something in between. Depending on the time you've been playing I would suggest you continue to use the C* & try some different reeds maybe plus a lot of practice. Of course there's always the chance your particular piece might be a bit off (factory problem)...you could have a teacher or a more experienced player try it for an opinion on that. Mouthpieces can get really expensive & you're not going to get anything much better or maybe not as good as your C* for $80....unless perhaps thru ebay where you might pick up a decent Vandoren.
Vintage pieces are terribly expensive, you generally cannot try them first, and once you get one you're stuck with it whether you like it or not unless you can resale.