Nikon enjoy a pretty high reputation for cameras (they compete with high end Canon's as the pro choice). Generally see good reviews of their kit.
The Fujifilm and Olympus ones are also pretty decent. Have used several Fuji's over the years (not the compact ones admittedly) and not had any problems or issues. And the first digital camera I ever used was an Olympus (only 1.2MP - get phones with more than that) and it was 100% reliable and very good picture quality given the limitations of the technolgy of the time (getting on for 10 years ago!).
Also my brother and his daughter bought Kodak cameras and have to say they do a very reasonable job. And if they can use them anybody can
Never used any of the others so would not like to comment.
One thing about the Fuji and Olympus. They use xD format cards in many of their cameras. Not quite as popular as SD or Compact Flash. I spent ages trying to find a card reader for the PC that did xD. But I see even Tesco sell the cards (and readers) so perhaps not the issue it once was.
One thing I would recommend is Optical Zoom over Digital Zoom. With Optical Zoom it is the lens that does the zooming so you don't lose any image quailty (if the lenses are any good). Digital Zoom however "zooms in" on the digital data which does reduce image quality. Similar principle to highlighting part of an image on the PC and enlarging it to full screen.