There's various theories about how the viewer's eyes scan a painting. In books on the composition of pictures, I've occasionally seen arrow lines suggesting how the eyes move. But how do the authors, usually artists, know that the arrow lines represent the true movement of our eyes. What tests have they done to support their theories?
There's scientific papers available on the subject, this one is interesting:
Here's an extract from section 5:
" It is nice to see that people fixated on
different things than what they remembered
more specifically. It goes to show that
sometimes cognitively people are thinking more
about what they are seeing in their peripheral
vision than what they are really fixating on. "
To find examples of good and bad composition, try "The Simple Secret of Better Painting" by Greg Albert.
In answer to your last question, the goal is to produce a picture that the viewer likes to look at.