Really, for the purposes you intend, even decent consumer camcorder will fit the bill.
Look for a camera with decent low-light performance, good image stabilization, ideally with a touchscreen to select your focus point and manual white balance capability. I'd also avoid something with a huge zoom range because usually the optical quality will suffer. For a wedding 10x with a bias on the wide (at least 30mm equivalent) is more important than the long end. The Canon HF G20 will fit the bill at $799 with current promotional offers.
I would still suggest a shotgun mic, and I've used a $30 Takstar SGC-598 with good success. You might need a hot shoe adapter for the G20 to accommodate a standard size hot shoe foot. But the mic can plug directly into the camera without the need for a separate audio recorder. A set of noise isolating headphones would be a good idea to monitor sound levels.
You will still need a gray card or some kind of neutral target to set your white balance at each location (don't use the brides gown as these usually have additives to make them appear whiter). And something to help stabilize the camera, such as a tripod or $30 Cowboy Studio shoulder mount (my daughter swears by the latter for cheap and effective run-and-gun video)