Look at more Canon models then... Of course, you will need to figure out what your maximum budget amount is first, then try to find a camera that will fit it.
As for noise, you actually want a minor amount, depending on the image, otherwise it will look flat. Noise has other purposes as well. When you look at a gradient, without noise it looks flat, with noise, it looks smooth.
As for the shake comment, I hope you're talking about shake compensation in the camera. Of course, you never should hold onto a camera and take the shot at less than 1/60 of a second. Below that, unless you're a rock, you will have at least some shake/blur on the image. That's what tripods are made for, so you can take slower shots and not ruin it by your motion. Even breathing can cause the image to become blurred.
Also, what sizes are you going to print? If you're only going up to 8x10, with some cropping, then you could get away with a 3.1-3.2MP camera. Ignore digital zoom, ONLY look at optical zoom. If you want to print out larger images, or you know you'll be cropping out a lot, then you need a camera with good optical zoom (to do part of the cropping before you take the shot) or something over 4MP.
Oh, and the RAW format means (at least on my Canon) that it takes more pixels and doesn't toss out any. I can get about 1500+ shots on my 4GB micro drive under the large-fine setting. If I go to RAW (large) then I can only get about 670 shots on the same drive. That does give me more image to work with, of higher quality (not less). The BETTER cameras offer you the option to capture in the RAW format as well as the jpg (and even TIFF) format.
Don't expect a sub $700 camera to perform as well as a digital SLR can. The two are not even in the same class. Digital SLR (or DSLR) is at least a step or three above the fixed lense cameras, no matter who makes them.