When I got my new MacBook, I bought the program iPhonedrive which is now called Megaphone. It worked very easily. Geordisjd (if I am spelling her name right) here on this forum told me about it. When you connect your iphone to the new computer, it will lead you through the process of getting all the stuff off the iphone and onto the computer.
http://www.ecamm.com/mac/megaphone/