iPhone 5 to 5c transition of calendar, texts, etc

So I'm moving from a 16GB iPhone 5 to a 5c with 8gb. I have about 13 gigs so some stuff is going to be cut. Also transferring providers. So I have everything backed up via iTunes as well as iCloud but I don't really understand how to pick and choice and force stuff to move over. I really need/want the calendar, contacts, and texts. I can move some photos manually later as needed. So my calendar transferred somehow (don't remember if it was iTunes or iCloud but it happened) but not all my old texts are moving over and neither is the calendar. Suggestions please.

update

it seems as though my calendar decided to populate after I left the phone alone for a while.

I wonder: will the text messages from the old phone do the same? I guess I have what I really need now--the contacts and the calendar. I can move over the photos I want manually I guess. Not sure what the best way to do that is though.