If you want to migrate your phone to a new account and take your iCloud data with you, start by saving any photo stream photos that you want to keep to your camera roll (unless already there) by opening your my photo stream album, tapping Select, tapping the photos, tap the share icon (box with upward facing arrow), then tapping Save to Camera Roll. If you are syncing notes with iCloud that you want to keep, you'll need to open each of your notes and email them to yourself so you can later copy and paste the text into new notes created in your new account. Then go to Settings>iCloud, tap Delete Account, provide the password to turn off Find My iPhone and choose Keep on My iPhone when prompted. Then sign back in with the new iCloud ID and choose Merge to merge the data on your phone with the new iCloud account.
iMessages have nothing to do with iCloud and as a result will not be effected by any of this.