I sense that tempers may start to flare when the phrases, "first new car", "buying a Z", "parents", and "co-sign" start being put in the same post. Not from me, but just to give you a heads up on what may be coming...
To answer your question, yes, a co-signer can help you qualify for better interest rates.
I would really suggest that you just go talk to your bank. They'll lay out what the terms are, and you can discuss whether a co-signer would help the rate. Because yes, there are definitely cases where you might qualify for the loan in general, but a co-signer would lower the APR.
I don't know about the names on the title. As joint-buyers, I would think that both of your names would be on the title. But I do believe that this varies from state-to-state. It may also depend on the bank too, since they're the ones who will have a lien on the title. I don't really know.
I'd try to finance it on your own, first. It's nice that your parents would co-sign for you, but if that's required to make the deal happen, then I see that as a sign that you're perhaps not financially ready to take out a $40K car loan. I don't mean to offend. Just a random forum poster's
.