My brother recently invested in an Olympus 510UZ and he's very pleased with it. 7.1 MP, 10X optical zoom, takes standard AA batteries, full automatic everything and has every conceivable manual over-ride for when/if you get a bit more adventurous

It's hard to beat Olympus optics and at the end of the day, the image quality depends on the quality of the lens. The quality of the image content depends entirely on the cameraman....and there is nothing any camera manufacturer can do about that problem

You can pick this up for around £150, but expect to add on some more for a couple of sets of rechargeable batteries and a memory card.
10x optical zoom is probably as high as you want to go. Even at that, you will need a tripod to get really rock steady shots at the extreme end of the zoom range. even if the camera has some kind of image stabiliser. Very little point in investing in resolutions much above 7-8 MP unless you are planning on running off poster sized prints.
One last thing, how portable do you want it to be ? Both this Olympus and the Fuji 5600 have to be worn around your neck or in some kind of camera bag. They aren't exactly pocket-sized. However, if you want decent photos it pays to have a camera you can hold comfortably and for that you do need something along the lines of these two.