You'll want to use Pangu, which to my knowledge, is the only jailbreak available for the latest version of iOS 7. It supports jailbreak for iOS 7.1 through 7.1.x. You can read more about that in this thread on "Can I upgrade to iOS 7 and run Pangu jailbreak?" The actual Pangu jailbreak can be downloaded here. Of course, any questions, feel free to ask. I'm not well versed in Pangu, but plenty of folks here would be able to help you.
I've been fighting with activating the stinking phone. I guess becuase I never update from 5.1.1, when I attempted to restore from a back up it would not take. So all my text messages are stuck on my 4S, i guess I could update it and back it up and then restore on the 5S.
But, im thinking after I JB I can transfer the messages over... now for the real fun.