Get a Moto X. It doesn't look that impressive on paper, but it's about the usability and experience. It's pure Android too, so no bullshit from the OEM's on there...pretty much a Nexus phone. The Moto G also just came out and already it's Motorola's best selling phone, it's just a cheaper version of the X pretty much. Also look at the LG G2.
Your contacts are sync'd with your gmail account. So just log into your new phone and they will come over, the apps you had will also then be installed on your new phone.
Photos are stored on your SD card, so just plug that into your new phone and that's that. Music will also be on your SD card unless you take advantage of Google Music's cloud storage, then it will be there as soon as you sign in with gmail.