No worries...you will do fine for yourself to buy a camera from any of the major brands - Canon, Nikon, Sony, Olympus, Fuji, Panasonic, or Pentax. Digital cameras are amazingly capable machines, and the average consumer won't notice much difference or get much different results from any of the major brands. Only experienced photographers truly need worry about whether one brand is incrementally better than another, because they are pushing the cameras to 9/10ths of their abilities and only when testing the limits will the differences really come out.
As for Cybershots - note that this is like a division name for Sony, representing all of their point-and-shoot cameras...hundreds of camera models have been sold under the Cybershot name, ranging from fixed-lens point-and-shoot cheapies to ultrazoom and prosumer models with manual controls and big lens barrels. Definitely stick to the model designations, like HX1, when referring to Sony cameras, because Cybershot is far too broad a category! (The same goes for Canon, with their 'Power Shot' name, or Nikon with their 'Coolpix' name).
The HX1 gets solid reviews, is a very flexible and versatile camera in a light and small package, and can do a few tricks other P&S cameras can't, so it certainly seems a good viable choice. The more important factors are: have you handled the camera and made sure you like the way it feels and the layout? And, is the price in your range? If yes, then you can't go wrong. The multiple-image-stacking feature for low light handheld capability is neat, as is the auto-stitched panoramas and the 10-frame per second burst mode...all neat tricks for this camera...and the nice big zoom range gives you lots of flexibility, from closeup animal shots on the safari ride to wide landscape shots across Bay Lake.
Best of luck!