Hi Sally, Most of the compacts are usually pretty good and affordable these days. Best advice is to go into a few shops and find a model that best suits your hands (comfort). Choose as many megapixels as possible. If you're unsure of what megapixels are these are like the dots that make up a TV screen if you look closely.
You want you can zoom into you camera picture and count the dots and you'll have 12 million or 8 million etc. Rather you than me though. The more pixels you have the better quality your image will be for blowing up really big and cropping etc. Flip side is they'll use more space when storing on your computer or camera.
Don't worry about too much else with the compacts as they bolt on alot of fussy stuff/features you probably won't use. Set your budget and get the most pixels for that. Well know brands like canon, olympus and nikon are good. Once you've found a good camera you like search online for the best bargin. Memory cards you need to buy separate.
Look at warehouseexpress.com for a good supplier who we use.
Happy Shooting!
P.S A year ago (2008) I got a cheap compact camera for holiday use and it's shock proof and water proof to 5m. Haven't tested the shock to its limit but took it diving to 10m and still working fine. It shoots 8 megapixel and I use it when don't wanna carry and SLR. It's an Olympus 850 SW and it gets some grief and still runs fine. Probably a few newer models out now but old models are still good if you're looking to save dollar.
Hope that helps.

I would recommend the Nikon P3 its an 8 megapixel camera and you can get a new one fairly cheap on ebay? I paid £45 recently for one for my collection. Another good buy if one comes up? Is a sony dscf717. This camera is only 5 megapixel but you can buy a cheap infrared filter from hongkong and take some stunning infrared images..Expect the camera to cost upto £70. This may seem steep but you have to remember when they came out they cost new £1000! It also takes excellent mpeg movies also in infrared too! An excellent choice is also Konica Minolta Z3. This is an excellent camera with a huge zoom range and good quality even for 4 megapixel.
Also lookout for cameras where the ccd has gone blank. As there is a free repair till 2011. Most of these are mainly older Nikon,Sony,konica minolta. there are others so you can buy these cheap as spares repairs then send it in for the free repair and you basically have a refurb model.I would avoid older fuji as fuji dont do anything free!
The only decent Fuji in my collection is my S7000 As its upto 12megapixel.