Restore the device again, when prompted to restore as new or from backup select from backup. iTunes will then prompt with the available backup options to restore from.
Sounds like you may have elected to not use the device as designed.
Contacts are designed to be synced to a supported application on the computer or a cloud service. If this had been done it would be a simply matter of syncing the back.
Relying on an iPhone for sole storage of pictures/videos is extremely unintelligent. Like with all digital cameras, pictures/videos taken with the device should be copied off the device to a computer regularly to ensure they are not permanently lost in the event the device is lost/stolen or simply fails.