True, it is also good to have an idea which tone means what. As far as I know it's: high-level, raising, falling-and-then-raising and falling (the shape of the dashes over i gives the hint) http://en.wikipedia.org/wiki/Mandarin_phonology#Tones
Agree on the last point -- at least, for Taiwan. In fact, those idealized graphs caused me a bit of a headache early on. Native mandarin speakers in Taiwan tend to drop the end of the 3rd tone, so it falls slowly then holds at the bottom for a minute, then rises slightly or even just cuts off.
shi1 = shī
shi2 = shí
shi3 = shǐ
shi4 = shì