Caroline,
You need to do some research (which is why your are posting here, of course!).
Like the others, I like dpreview.com. They have a neat feature where you can compare the features of digital cameras side by side that may help you evaluate your options.
Here are some things to consider....
I will be mainly using it for wildlife, landscape, and people. I would really like a camera with a really good zoom,
This is a tough task. In order to discuss this, you have to understand the concept of the focal length of the lens. Long focal length lenses allow you take pictures of things far away with a narrow field of view (like looking through a telescope or binoculars) while short focal lengths give you a wide field of view which allows you to include more of an area in your shot.
The effect of lens focal lengths, however, vary with the size of the sensor in digital cameras, so you can't just compare the focal lengths printed on the lenses of two different cameras. In order to make comparisons, people tend to use "35mm equivalence" in order to standardize the numbers and to be able to evaluate the effect the focal length will have. (These numbers are based on the effect that would be seen in a 35mm film camera since most photographers are familiar with lenses for these cameras).
For wildlife shots, you will need a long lens (at least 300mm in 35mm equivalence - 400mm would be better).
For landscape shots you need a wide angle lens. I like something less than 28mm (in 35mm equivalence).
For people pics, any lens in the 50mm to 100mm (35mm equiv) range will work fine. If you like to photograph big groups, you might need a wider lens (your landscape lens, for example).
Now the problem is getting all of this in one lens! Finding a lens which gives you good images at both extremes is difficult. There are some that do, but the image quality they produce isn't as good as that produced by lenses with shorter zoom ranges.
It is hard to make good lenses that can zoom from wide angle to telephoto (long focal length) that maintain good image quality across the range, so all zooms are a compromise of quality and flexibility. In short zoom ranges, it is easier and quality is better at both ends, but in long zooms (often written as 50-500mm or 10X zoom) you lose some image quality.
So you are probably going to have to compromise if you want to cover this range. I suggest looking for a camera with a zoom equivalent in the 28-200mm (35mm equiv) range that has a 5MP or higher sensor. Then you can get your landscape shots at 28mm and shoot wildlife shots at 200mm and then crop to get frame filling pictures.
I have an older digicam which has a 38-380 zoom and it just isn't wide enough to get good landscape shots, IMHO.
and one that can take motion shots very quickly.
Getting good motion shots depends on several issues.
First, you need a fast shutter speed which almost any capable camera will have. Really you probably would never need a shutter speed faster than 1/2000th of a second. (Yes, there are cameras that can provide shutter speeds of 1/10,000th, but that sort of speed is almost useless, especially without high-speed synchronizing flash units - which cost more than the camera!) So any camera that can take pics at 1/2000th or less is fine. A good flash is also helpful for this.
The other issue is how fast the camera responds. Many point-and-shoot digitals suffer from "shutter lag". This means you press down the shutter release to take a picture and it takes some time before the camera actually takes the picture. How much time varies from camera to camera, but it can be as much as 1/2 a second. If you are taking action shots, most of the action will have changed/moved by the time the camera finally takes the photo. OK for shots of people sitting around, but you wouldn't want to try and get a pic of someone hitting a baseball that way.
Even worse, some cheaper cameras take as long as 5 seconds to turn on. Imagine seeing that great shot of whatever you have been waiting for then having to wait 5 seconds for the camera to turn on and another second for it to actually respond to you pressing the shutter release! It can be frustrating.
Make sure you read about the response time of any camera you are considering. I missed a lot of shots with my older Olympus C-700 UZ because of this. It was almost impossible to get a tongue flick on a snake, for example.
Another issue affecting this is the ISO setting of the camera. Most digital cameras can shoot pics at settings of 100, 200, 400, 800 ISO. Some go as high as 3200. Higher ISOs allow you to take pictures in less light and with faster shutter speeds.
However, just because a camera has that setting doesn't mean it is usable. At high ISOs, the image becomes grainier and grainier (think newspaper pictures). Some cheaper digital cameras are not usable above 400 without serious image degradation. Good DSLRs can generally take pics at 1600 and you can't tell the difference. So you need to see how grainy pics are at higher ISOs with the cameras you are comparing.
Generally, DSLRs provide what you need, but they are expensive. In order to buy a body (I suggest the Nikon D70s or the Konica Minolta 5D as excellent starting bodies), you have to shell out $700. You general use zoom (say 28-200 in 35 mm equiv) costs another $200 and then you want your 300mm wildlife lens which is another $400. Pretty soon you have $1500 invested in camera equipment. However, you can buy a few pieces at a time and add the other things later. The other advantage to this system is that a few years down the line, you could keep all your lenses and other accessories and just buy a new 25MP camera body when they become affordable.
You can also get some very good inexpensive (under $500) point-and-shoot type cameras (some of the better cameras in this range are sold as "advanced" digital cameras rather than point-and-shoot). You may not get the total zoom range you want (make sure you get the wide angle!) and it won't be as responsive as a DSLR, but you can get a very satisfactory camera. The image quality isn't quite as good because the sensors are smaller, but unless you make a poster sized print and compare them side by side, you won't notice a difference.
There are some very good cameras like this available. Unfortunately, everyone will tell you "I have the X-brand 2304g" and it is a great camera. Generally, these people have only ever used that camera or possibly 2 or three others types for comparison! How do they know it is a great camera???
I have only ever used the Kodak 3700, Olympus C-700 and C-750 point-and-shoots as well as the Nikon D70, Canon 20D, and Konica Minolta 7D digital SLRs as well as half a dozen film SLRs. All were capable cameras, but I don't know what to recommend to you because I haven't even picked up MOST cameras. But there are LOTS of others out there. That's where a good review site (like dpreview) will help you out. The people that do the professional reviews have used hundreds of digicams and know the difference.
I know this seems like a lot to consider, but if you spend the time to figure out exactly what YOU need, then you will be much happier with your purchase. Good luck, and show us your pics when you get them!
Remember - good photographers take good photos, not good cameras.
Chris
-----
Chris Harrison
San Antonio, TX