Can I jailbreak if I just updated to the new ios?
the new jailbreak supports iOS 6.0 - 6.1 so you are good.
Will I have to re-install the apps I currently have?
Nope, as long as you back up your phone to iTunes you won't lose anything. The GUI will guide you through the process and tell you what to do.
is there anything else I should know before I move forward?
Absolutely make sure you have backed up your phone in iTunes before doing anything. That way if you mess up or if you want to go back to stock iOS and do away with jailbreak you will have something recent and good to go back to.
It also wouldn't hurt to check this out preparing for jailbreak