Well, after a long time of researching, reading reviews, and examining sites that compare side by side photos of cameras, I decided that the camera that has the features I wanted was the Canon SX130 IS, which is the upgraded model of the previously common 'top pick' camera, the Canon SX120. It is a 12 megapixel camera, with 12x optical zoom, image stabiliser, and a range of other neat features. Mostly though, it was the best image quality 10+ zoom camera in my price range.
I nearly spent double the money on the Canon SX30, which is a camera with a bucket load more features than this one - however, comparing photos of the same scene, in the same lighting, side by side, I found that the more ISO increased, the more noise and distortion appeared on the SX30, while at ISO 1600, on the same scene, the SX130 was clearer and smoother than any other zoomer camera I came across. As I do a lot of miniatures toy photography, smooth indoor photos was something I wanted. I also really like the colours of Canon photos.
A great site I was put onto is this one: http://www.imaging-resource.com/IMCOMP/COMPS01.HTM
You pick a camera on the left, and a camera on the right, and then select the same photo for each camera, and you can see, quite clearly, the differences between any two cameras in the lists. Clicking on the photos makes them come up full size in a scrollable window on their half of the screen, for seeing the 100% photo size image quality of the cameras. Comparing the SX130 to any similar long zoom camera at 1600 ISO, and you will often see tons of noise in their images, compared with the SX130. However, if you don't need a long zooming camera, some of the shorter zoom cameras have crisper, clearer images than the SX130, so they can be worth looking at too.
Of course, some SLR cameras are on the comparison list as well - and when you compare the best quality of a compact camera image (even at 80 ISO), to an SLR camera all the way down at 1600 ISO, the SLR still beats the compact's image quality by a mile! The SLR's are amazing. They are also out of my price range :) So I'm very happy with my zoom camera.
Anyway, here's some photos! I am not uploading them at full size (which is 4000 pixels wide!) I am resizing them, but you'll get a bigger image by clicking on a photo. (opening pics in another tab or window is always a good idea)
Here's some examples of the zooming. The first photo is no zoom, from my house. The second is full optical zoom on the flower in the middle. The next is full digital zoom on the bee on the flower (still standing at my house).
I should note that for these next three photos, I clicked 'auto adjust' on my computer, so the original photos didn't have as much contrast as these pictures - but these three photos are more to show what the zoom looks like.