Your best bet is to go to a camera store and try a bunch of cameras to see which ones you like. I can suggest a few general points to consider, however. First, the kind of photography you seem to do most often is better served by a decent wide-angle lens than by a long lens. If you think of the problems you have when trying to get the whole family reunion to fit into the frame, you'll know why wider is better. a 24mm equivalent lens is ideal, but anything 28mm or less will be fine.
Second, you should pay attention to the f-stop size at the wide end of the range. Those portrait-style photos of an individual, where the person is in sharp focus and the background is blurry require a small-number f-stop. This is typically a weakness of less expensive lenses. Ideally, at the wide angle end, your lens should be able to open to f2.8 or better (2.0 is "better" than 2.8, 1.4 is "better" than 2.0, etc. in this context). Usually, the superzooms will have a longer natural focal length than the pocket cameras, so the same f-stop will give you better separation between in-focus and out-of-focus than the smaller cameras will, for reasons that are beyond my ability to explain.
Third, while the red-eye suppression keeps getting better, you want a flash that is as far from the lens as possible. On a typical superzoom, the flash pops up to give you better separation between the flash and the lens. That cuts down on red eye. The closer the flash is to the lens, the worse red eye will be.
Fourth, you want as strong a flash as you can get. The manual will tell you how far the flash is good for. Typical pocket cameras are about 10 feet. A superzoom will typically be good for up to 25 feet or so. This makes it a lot easier to take those indoor group flash photos without having everybody look like they're in shadow.
Fifth, the faster your camera is (higher ISO that isn't too noisy, wider f-stop lens) the more likely you can take the photo without using flash. Generally, no flash is preferable to using flash -- especially flash that is built into the camera. So get as fast a lens (smallest f-stop number) and as good performance at high ISO settings as possible.
If you are interested in getting deeper into photography, I would think that the first thing you might consider beyond the above is a camera with a hot shoe. This is a camera that will allow you to attach an external flash unit, which means you can take bounce flash photos or attach a diffuser to the unit to improve the appearance of the flash photographs. Both approaches are easy to master, but require you to carry more equipment and "fiddle" more with the equipment, especially while you are learning how to use it.
All in all, I would expect that a superzoom might well be a better option for your use than a compact camera. But you really need to handle them to decide whether they are the sort of thing you'd be comfortable carrying around, as they aren't pocket cameras.
Last edited by tclune; Aug 3, 2009 at 8:45 AM.