What kind of a difference is picture will I see when moving from a cheaper camcorder (without 3CCDs, I'm guessing that means they have 1, but I'm wasn't sure) to a Canon with 3CCD? Will it be in picture quality, less artifacts, better colors, or what?
You're correct in asssumiing that the less expensive camcorders have only one imaging chip, although this technology is improving all the time. Consider the new Sony HDV one chip camera called the HVR-A1U. Impressive little 1080i HD camcorder for the money.
Traditionally, going to a 3 chip video camera will give you a much better image than with just one chip. The light entering the lens of a 3 chip camera is split into the 3 primary colours: red, green and blue. The colours are then recombined before the image is recorded. The resulting image is cleaner, sharper and is more saturated (richer colour).
The second big reason for stepping up to a 3 chip camcorder is better optics. The lens will be of a higher quality and it will admit more light because it's usually much wider than the lens of a small 1 chip camcorder. Get used to saying this to people about your new 3 chip camcorder: "It's all about the glass."