The amount of memory is very important on the laptop. Try and find one that will have just one 512 MB stick in it. Then you can buy your own second RAM stick at half the price (or less) of what the laptop guys will charge you. "Marketing 101 give away the Barbie dolls and charge a fortune for the dresses."
Back to the fun stuff:
Nikon has been very agressive in pricing lately. i.e. more bang for your buck (or pound). The advantage to Nikon is in the optics which is not that important for general usage. The Nikon might also have better features in it than a Fuji. Better exposure, faster focus, etc.
When you find a few possible choices post them and we'll do a feature comparison. (Camera and Laptop) Everybody here just loves helping other spend their money.
Since the kids are using it I would look for a camera with solid construction. i.e. Battery, memory slot covers, etc that are robust enough for a lot of handling. Rounded corners (less likely to crack) when bounced around.
Batteries - make sure the camera uses standard AA NiMH batteries, preferably 4. Lithium batteries last a lot longer but are very expensive compared to alkaline or NiMH. Rechargeable lithium are $50 each and you will want at least one spare.
I love this site. Search for your spec's and brand comparisons. Prices and sellers are USA unfortunately.
http://www.dpreview.com/reviews/compare.asp
If you like the traditional SLR shape:
Fujifilm FinePix S5200 Zoom
Fujifilm FinePix S7000 Zoom
If you are into the cigarette pack look:
Canon PowerShot A610
Accessories for either one:
8 pack niMH batteries and a charger $25
256 Mb memory card $25-50 (higher for the fuji, it uses xD instead of SD memory)
Avoid Konica-Minolta. They are leaving the camera market.