My pick would probably be a Panasonic micro 4/3rds camera: the G3 or G-5, or, GH-2 or GH-3.
The Panasonics are very good still cameras, but are also known for their video capability. These 4 models will also allow you to change lens if you want. The GH-3 is weather sealed but the most expensive-body only-@ $1300. The least expensive-the G3-body only @ $250. Panasonic, and most of the major camera makers, offer pretty decent digital cameras often referred to as super-zooms; digital cameras with general video capability with a fixed, but wide-ranging zoom lens. A website called Digital Photography review generally tests and reviews many of cameras. B&H Photo is a great online retailer to check prices.