given your budget, I think the Fuji SX1 will be a bit too pricey...
Maybe I'm gonna type a lot of info you already know, but just in case, here's a broad overview of the possible directions you might go.
For an all-in-one camera, superzooms like the Canon SX40 are pretty good indeed, since they cover a wide range of possible scenarios. Low-light shooting and shallow depth of field (blurred background) aren't their strong suits though. The so called Travel Zooms like the SX230 are also very capable, but are often less intuitive to control manually; if you want to set a slower or faster shutter speed than what the camera thinks is necessary, for instance, cameras like the SX40 make that a lot easier. On the other hand, the smaller Travel Zooms will fit into pretty much any pocket whereas the Superzooms will often require a small camera bag.
For your budget and wishes, you could also look at a mirrorless camera with a large sensor (like the Sony NEX series, or Panasonic / Olympus / Samsung's competition) with a kit lens. This would cover most shooting situations, but you'd typically get a zoom range of roughly 28-84mm equivalent, so not nearly as long as the small-sensor cameras. Big upsides are their high ISO abilities and shallow depth of field abilities, and some of those cameras also have easy manual controls.
In between the small sensor cameras and the large sensor mirrorless cameras is a small class of enthusiast-aimed compact cameras with fixed lenses and a sensor that's larger than usual for compacts, but not quite the size of a mirrorless camera's sensor. These include the Canon G and S series, Nikon P7xxx series, Panasonic LX series, Olympus XZ1 and Samsung TL500 (aka EX1). They're usually small enough to carry in a coat pocket, and many of them have longer zoom ranges than the kit lenses for mirrorless cameras, though not as long as Superzooms or Travel Zooms. They do tend to have faster lenses than the high zoom compacts (larger apertures, allowing them to let in more light which is useful in low-light situations and for getting shallow depth of field), which helps them punch above their weight (sensor size).
Raw is like a digital negative, whereas a jpeg is fully developed in the camera. If you're not completely satisfied with the colour or exposure or sharpness of the photo, raw files will allow you much more room to correct this through software like Photoshop or one of its competitors. Jpeg files can also be corrected to a certain extent, but if you go too far you'll get a horribly ugly image. Basically, raw allows you more control over the end result but requires a bit more effort, while jpeg doesn't require any effort unless you want to correct something. All of the cameras in the enthusiast compact class and the mirrorless class can shoot raw files, whereas not all travel zooms or superzooms can.
I'm looking for a compact camera with the below specs, if possible 
