Originally posted by groovyg So, I understand that sensor size and sensor noise have an inverse relationship.
Correct, as long as you are using identical shooting parameters (e.g., the same f-stop).
If you use equivalent shooting parameters, the noise is exactly the same (bigger sensors do not have inherently less noise, they simply allow the use of brighter lenses).
Originally posted by groovyg I've also heard that on a given sensor size, a lower megapixel count with bigger pixels produces cleaner images.
This is incorrect.
While it is tempting to believe that smaller pixels receive less light and hence are noisier, leading to a noisier image,
the increased number of pixels offset the higher per-pixel noise. In other words, while per-pixel noise is higher with higher resolution sensors, their per-image noise is (pretty much) the same, everything else being equal.
Sensors often are based on different technologies and hence differ considerable in their noise performance. But in principle, the number of pixels on a sensor is not a factor for noise (within reasonable limits).