Protestants, baptism and the covenants

I'm not sure that this is right but it is seeming from my reading that:

• Luther thought that the New Covenant is with every individual. It may be rejected by unbelief but the promise of the New Covenant is for all.
• Reformed theology seems to see the New Covenant as being with believers and their children (unless they reject it). However, I may be wrong here as while it is clear that they see believer's children as in the 'covenant community' I'm not sure that it is the same thing as thinking they are in the covenant.
• Credobaptists believe that the New Covenant is with believers only.

If this is a true summary then the different beliefs about baptism are simple to explain. However, I am 90% sure that my sweeping generalisation is wrong. But I'm trying to get things right in my head as I go.

Please, please, please correct me where I'm wrong.