Q: Should my wife and I have separate ID's for both Apple and iCloud?

Yes. You will need to transfer contacts to both accounts. This might help:

how can i transfer my contacts to another apple id?

Also you will need to create another Apple ID:

https://appleid.apple.com/account

Hope this helps,

- Fin

Oh ya. If you want to share apps, music, etc., you can set up Family Sharing:

Set up Family Sharing - Apple Support

Apple IDs are iCloud IDs. You should get separate Apple IDs and then, if you want to you can turn on Family Sharing, so you can share purchases. That is what I recommend if you started out sharing an Apple ID.