"Are there different types of live rock?"
Yes. There are many different types, all of which I am not familiar. However, my 55 has both Fiji, and Gulf live rock. Buy locally cured live rock, and you should be okay. If you buy live rock off of eBay, or online, there will be some die-off during shipping, and this could mini-cycle your tank. I've had damsels, they are too aggressive. I now have two small 1" true percula clownfish, and they so far are doing great. No fighting or aggression so far. Other good fish are green chromis. They are quite beautiful, and from what I have read/heard, not that aggressive. But remember, no matter what fish you choose, make sure that the tank is completely cycled prior to introducing any livestock.
Jared