When I went from my Iphone 4 to my Iphone 6, I just did a backup to Icloud on my 4 and then restored from the backup on my 6 and it was all there, just like cloning my old phone.
That's exactly how it's meant to work. As far as emails, they should be stored on whatever email server/service you use, and your phone just controls how much email to fetch from the server. They should be fine as well.
Now this is a CDMA phone (I have no SIM) but technically I think it is supposed to work the same regardless of the phone technology.