I never used external flash. Please tell me what to look for in an external flash for my Panasonic DMC-FZ200 camera.
If you want full TTL (automatic) flash with the flash mounted on the camera's hot shoe or connected to the camera's hot shoe via an off-shoe cable: you need a "dedicated" Panasonic flash. The Olympus flashes for 4/3 and µ4/3 systems use the same pin arrangement and protocol as the Panasonic flashes and are generally said to be better and cheaper than the Panasonic flashes. Any third party flash "made for Panasonic" or "made for Olympus" should also work.
If you want manually controlled flash, either on or off the camera: pretty much any flash with a center pin that has a trigger voltage your camera or wireless trigger can tolerate will work. The trigger voltage is important! If the flash has a higher trigger voltage than the camera can tolerate the voltage applied by the flash to the hot shoe can fry your camera's electronics!