@amybatt, what you have said makes me worried about what else the guy taught you, because keeping the ISO to below 200 is patently wrong for any kind of fast action or most situations where long focal lenghts are used.
Also, I am not sure what this new camera of yours is. Knowing will make it a lot easier to understand how bad noise is going to be at higher ISO's.
So, here are some general guidelines:
When hand-holding a lens, the old rule of thumb was that you need a shutter speed of at least 1/focal length. This is for a 35mm (so-called full-frame) camera. In this regard, a smaller sensor has the effect of increasing the affects of camera shake, and thus you need to multiply this by the "crop factor". Having said that, it is only a guideline, some people need to half that shutter speed, and others can dounle it. It also doesn't take Vibration Reduction or image stibilisation into account.
The above is just to prevent movement blur from your own shaking, and doesn't take subject motion into account.
For subject motion, to freeze that cheetah chase we would all love to photograph, you will need at least 1/1000th of a second. The same speed applies to large birds in straight and predictable flight. For smaller birds (say dove-size), you will need at least 1/2000, and for the really fast smaller birds like Kingfishers and sunbirds, 1/3200 to 1/4000. For hummingbirds (which I have never even seen), some say 1/8000 is not enough.
So while it is definately true that the lowest ISO will produce the best possible image quality, what has been said above that a sharp photo with some noise is better than an unrecognizeable blur of a once-in-a-lifetime moment is definately true.