Hi Jeremy! I'm Ryan. This will be a good start, and probably finish for you regarding all the information you could ever want or need to know about the top end of your engine, and a few other things! Fairing repairs included...which I'm working on now!
Welcome to the site! I myself am a newbie rider and I also picked up an FZ600 as my very first bike. A lot of power for a learner if you ask me...definitely have to remind myself to slow down often when I'm on it. The snow does a good job of keeping me off the streets in the winter up here though....
I did a complete top end rebuild, along with the carbs, in about a month, started mid-December and it's already back in and running. Was my first ever rebuild and I did it from start to finish by myself. I got lucky finding this place and meeting some awesome people who were willing to offer advice when I needed it (and it was often! lol) and I managed to get the engine back in and fired up no problem! My issue was a stripped bolt hole and burning oil... Be careful though, it seems like once you start replacing one thing, you want to do the next, and the next, and the next.....haha
Like sniff said, check the shock setting, it's variable, same with the fronts, you can add air to the front and up the PSI to increase stiffness.