For fireworks you will definitely need a tripod. I would probably start shooting in Speed priority mode with about a 2-3 second exposure and work up from there or switch over the Manual mode. It really depends on how much motion/movement of the fireworks you want to capture. You should check out some firework shots on flickr and look at their exif data to get a feel of what others are using too.
Oh, and for the photos above, remember the rule of thirds
