First ask yourself what sort of camera you want: compact, bridge, SLR or any shade in between. Then think about other considerations like: does it need to be weatherproof; will you be spending a long time (days) away from the mains; do you have any existing flash cards that you want to use; do you want full manual control; might you want to use an external flash; might you want to use a cable release? If you think you're going to want to take any photos indoors then have a good read of this article:
http://www.dpreview.com/articles/compactcamerahighiso/
You'll see that Fuji makes some excellent sensors. But beware, not all of their cameras use their own sensors!
You can get a Fuji S6500fd (known as S6000fd in USA) from around £150. This has the same sensor as the F31fd mentioned in the article but with a manual zoon lens on the front. Why on earth the manufacturers thought we needed motorised zooms I shall never understand! I'd avoid the S5700 as this has a poor, non-Fuji, sensor.
But beware! Fuji is very likely to release the successor to the S6500fd in the next couple of weeks. If you're thinking of heading this direction then I'd hang on for a wee while.
Also check out:
http://www.dpreview.com/
http://www.steves-digicams.com/
http://www.dcresource.com/
http://www.imaging-resource.com/
and, in particular:
http://www.steves-digicams.com/best_cameras.html
And don't forget to factor in the cost of spare batteries, flash cards and, if appropriate, skylight filter and tripod.
IMHO, it's a good idea to get a camera that uses standard AA cells rather than some proprietary (expensive) battery. If you choose a camera with AAs then definately get some Sanyo Eneloop cells and a NiMh charger. These are the Mutts Nuts.
Note that I've have a Fuji S9500 so I'm biased
