In hindsight, I think that bit of advice about setting your camera on manual or Av mode might have been a touch misleading. If you leave your camera on full auto in an environment like that, it should still do a pretty good job of maintaining similar brightness levels between zoomed-in and zoomed-out shots. The only thing is that the camera’s metering system could get fooled by things like dark shadows (causing it to attempt to brighten the image to compensate) or a bright patch of sunlight (causing it to attempt to darken the image). I find that in a situation like that, it’s often a good idea to take a few shots of drastically different areas on full auto, see what the camera chooses for aperture, shutter speed and ISO, then manually set the camera up somewhere between the two extremes.
According to the specs from Canon, your ISO range is actually 80 to 1600, pretty good for a P&S.
The optical zoom range on that camera is really quite exceptional, and with the image stabilization, you should be able to get quite good telephoto shots with it if you’re shooting hand-held during the day. The aperture range is decent for what it is, but it means that if you’re at, say, a sporting event and you want to make sure the wide-angle shots and the zoomed-in action shots of individual players all have a similar brightness level, you’d do well to put the camera in either manual or aperture-priority mode and manually set the aperture to f/8. Fortunately, your camera has full manual control (with the exception of manual focusing, but that’s not too hard to get around).
I don’t know how this particular camera behaves in low-light situations, or whether its images are at all useable at 1600 ISO, but small-chip cameras in general tend to require more image smoothing. Your photos are never going to match the quality of a full-frame 35mm DSLR, but unless you’re submitting images for publication, it shouldn’t ever be an issue.
As for inexpensive lighting, you’re going to be limited to either natural light (sunlight and/or daylight), or continuous artificial lighting. Your camera doesn’t have a hot shoe, so strobes of any sort are out, and I really wouldn’t bother with the built-in flash except in strong backlight situations (middle of the day in the middle of the summer, you’re out in the desert shooting up into your friend’s face with the sun just behind his head, for instance). You can get 500-watt and even 1000-watt continuous work lights for relatively cheap at most building supply or hardware stores. They come with built-in telescoping stands and have either two or four lamps that can swivel and tilt independently. The tricky part with those is that, because they’re usually tungsten lighting, they tend to get very hot, so you need to be very careful about putting diffusers in front of them.
Other cheap tricks for lighting: get a few inexpensive light stands (eBay is a good place to shop for those) and a pile of A-clamps, the kind with rubber or plastic tips (back to the hardware store), then get a couple of 4-foot by 8-foot sheets of white foam core (any decent art supply store should have this) and make reflectors out of them to bounce light into otherwise shadowed areas of a scene or portrait subject. (Note that if you’re taking this rig outdoors, you may want to bring sandbags along if there’s any possibility of even a light breeze, and I wouldn’t even consider going outdoors if the wind is strong enough to move medium tree branches.) Similarly, you can cut a hole in a large sheet of black foam core and tape a sheet of wax paper over it to make a scrim that you can shine your studio lights through in order to diffuse them and soften the shadows that they throw. Again, take care how close you position your lamps to the scrim so as not to start any fires. Finally, a sheet of white drawing paper (not watercolour paper, since that’s usually not very bright) taped to a wall opposite a sunny window with painter’s tape makes a great bounce fill if it’s too tight a space to fit your foam core reflector.
One last caution: do not mix daylight/sunlight with your continuous lighting. Sunlight is somewhat cool-looking. Light from a clear sky is even cooler (the sky is blue, after all). Light from the worklights (or any incandescent source, like lamps or overhead light fixtures) is going to be quite yellow, even orange if it’s dim enough. Your camera won’t be able to colour-correct for both of those colour casts at the same time, so it’s either going to choose one or the other (in which case half of your image is going to look “proper” and the other half is going to be either strongly yellow or blue) or it’s going to try to split the difference (and you’ll have a slight blue edge and a slight yellow edge to everything). If you use all of one type of lighting, your camera will be able to balance for that, which is especially important as you don’t have the option of shooting RAW and adjusting the white balance in post.