What I would look for in buying a new camera (last one bought Panasonic TZ3which I can recommend).
Megapixels - usually 6 is the base now
Size of screen - how easy is it to see in bright daylight. Currently I think only Canon still puts view finders on some of their cameras.
Type of memory card - far the cheapest is SD and is becoming the one the majority of point and shoot cameras take.
Telephoto lens - you would use this more than you realise. Bridge cameras (like my Canon IS S3) has a powerful 12 x zoom which is so handy. However, it does make the camera bulky and there is no way it will fit in your pocket. My other camera the Panasonic TZ3 has a 10 x telephoto lens but this is a whole neater camera which can fit in your pocket.
Video capabilities - many cameras nowadays can double as video cameras. I used my Canon camera last year to act as a video camera as well as stills. It produces excellent pictures and can zoom in whilst recording. It is also extremely easy to import into programs to produce dvds and combine them with the photos. The TZ3 doesn't zoom in whilst recording but does offer a bigger picture.
Battery life - Usually the cameras that can take the rechargeable AA batteries have the longest battery life. I think my Canon can take about 550 photos, lasts for ages any way. The Panasonic has a flatten battery (lithium) that lasts for about 250 I believe.
Image quality - should have had this at the top really. The best way to judge this is to read loads of reviews which will compare different cameras to get an idea on the best.
Cannot think of anything else at the moment. Basically once I on the search I just research loads of cameras till I get a clear idea of the market leaders with the particular features I want.
When you in the market for your new camera, buy a camera magazine with ratings for the current models, research on the internet with the camera review sites plus places like
Amazon, these will all give you an idea on what is the best camera available in your price range. Both the cameras I bought won loads of awards and I have not been disappointed in them. The TZ3 price is dropping like anything at the moment because the newer models are out which is another thing to think about. Usually Spring is when all the companies start releasing new models (not always) so older models prices can fall as the new stock comes in.