To prevent both phones from ringing, go to Settings>Phone>Calls on Other Devices, and turn that option Off. As LACAllen indicated, if you have the same Apple ID signed into iCloud, then Messages, FaceTime, Notes, Contacts, Calendars, etc. will be shared between the devices since by signing on the same ID, it indicates that it is one owner who wishes to share that content.
If you don't want to share that info, then create a new Apple ID for one of you and sign the old ID out of those apps above, and sign in the new ID. When you sign out of iCloud it will ask if you want to Keep the Contacts on your phone. Say yes, if you want to then merge those contacts into the new iCloud account. When you sign it on, it will ask if you want to merge them.
You can keep the same ID signed into the iTunes & App Store if you want to share purchases. But it is best to have separate IDs for all of the iCloud functions mentioned above.
The only other thing that will be deleted when you sign out of the old iCloud account is the Photo Stream. The Camera Roll photos (which are the photos taken on that device) will remain there. The photos in the Photo Stream album will no longer be there, but they will remain on the other device. You can use iCloud Sharing if you want to share any of the photos that are no on the device's Camera Roll.
Best of luck,
GB