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To transfer everything from your old phone to your new phone back up your old phone to iTunes on your computer. Then, when you're setting up your new iPhone you'll be asked if you want to set it up as a new phone or from a previous backup. Chose the backup option and select the backup of your old iPhone. After set up is finished , your new iPhone should be a copy of your old iPhone, with everything the old phone had.
Shouldn't be a problem. Though depending on what you have on your jailbroken device, some of your jailbroken plists may transfer over. Sometimes it can cause issues, but if you remove the tweaks prior to backing up the device, you'll be fine.