To better explain, we have a Nikon coolpix, I guess a point&shoot. It doesn't do good with lots of lights, darkness, motion, or really anything. It takes way to long to take a picture, so we always end up losing the moment.
My daughter is very involved in sports, so we need one that does well in gyms, she also plays golf so we need a good motion one.
Whenever we are at WDW we love to take pictures of the castle or good picture areas that are usually shaded, and our camera never works for the shade, fireworks, lights, or parades.
We just really need a camera that can take wonderful pictures, works quick, zooms wonderfully, and has not much of a problem with lighting. Not the best of the best, but the cheapest one that will do the job for those must have picture moments. We just need a camera that does all of the above with about 3 1/2- 4 stars out of 5.
Thank you, and please help, your advice is greatly needed and appreciated!
As previous replies have mentioned, these are the types of pictures that a dSLR + a good fundamental knowledge of photography (ie. shutter speed, aperture, ISO) can easily capture. Although you can capture these pictures with a point-and-shoot or a bridge camera, a dSLR makes these photos lots easier to capture. I'll address the points in the order that you mentioned them.
In general, point-and-shoot cameras have noticeable shutter lag and cycle times.
Shutter lag is the time from the press of the button to when the camera takes the picture. The shot-to-shot
cycle time is the time it takes the camera to take 2 successive photos, 1 right after the other. As you have noticed, many people are often frustrated at the long shutter lag and the cycle times of point-and-shoot cameras.
This is where dSLR cameras excel. dSLR cameras have almost instantaneous shutter lag (ie. once you press the button, the camera immediately takes the picture). dSLR cameras also have very short shot-to-shot cycle times, so your camera is always ready to take the next shot.
You mentioned that your daughter is in sports. For sports, you'll probably want a camera that has a fast continuous burst mode. Consumer-grade dSLR cameras have burst modes that range from 3 to 8 frames per second, which is sufficiently fast enough to capture most sporting events.
In addition, for sports and especially for indoor sports, you'll likely need a lens with a large aperture (small f-number). Large apertures allow more light into the camera. Because you've got more light coming into your camera, this allows you to use faster shutter speeds to capture fast-action sports. For indoor sports, you'll want to increase the ISO on your camera, which allows the camera sensor to be more sensitive to light. The relationship between aperture & shutter speed & ISO is what you'll learn about in any Intro to Photography class or book.
For pictures in shaded areas, you might consider using flash. This is where your foreground subject is located in the shade, and the background is brightly lit by the sun. The reason why these shaded pictures appear very dark is because the camera "thinks" that it "sees" a lot of light from the sunny background. The camera does not know that your subject is actually in the shade. In situations like this, using flash is called "fill flash." You can use either the pop-up flash that is built into the camera, or you can use a more powerful external flash.
For fireworks, ideally, you'd want to use a tripod because you'll be using very slow shutter speeds (like, 2 to 10 seconds) to catch the fireworks trails. There's no way you can steadily hand-hold a camera for that long and still get a sharp picture. Actually, you can place your point-and-shoot camera on a tripod and capture good fireworks photos.
On another thread earlier today, you mentioned that you wanted to know what the best of the best camera was. However, in this thread, it sounds like you're no longer interested in the best of the best camera anymore, but rather "the cheapest one that will do the job for those must have picture moments." I guess I'm a little confused.
If you're interested in going the dSLR route, then the "cheapest one that'll do the job" will be any of the entry-level dSLR cameras. Canon's T3 and T3i cameras, for example, are entry-level dSLR cameras. You should also consider entry-level dSLR cameras from Nikon, Sony, Pentax, etc. Any of these dSLR cameras will make it "easier" to capture the pictures you mentioned above, regardless of brand.
Even though I've raved about dSLR cameras, owning a dSLR camera does NOT automatically make your pictures better. Instead, I would suggest learning the basics of photography (ie. shutter speed, aperture, ISO). There are literally dozens of "Intro to Photography" books available in the bookstore and the library. You can watch photography YouTube videos. You can find "Intro to Photography" Web sites. You can take "Intro to Photography" classes.
No matter what camera you end up buying, the basics of photography are still the same. These are what will make your pictures better.