While I did cite that original study which lead to the idea of life starting off as a "primordial ooze", as a person of science, I don't necessarily subscribe to it.
Scientists are always in pursuit of explanations to impossible questions, and while this study provides us with a starting point, it falls short in some key aspects. In the Miller-Urey experiment, a mixture of gases, including methane (CH
4), ammonia (NH
3), water vapor (H
2O), and hydrogen (H
2) was used to simulate the most abundant molecules presumed to exist in the earth's atmosphere 3 to 4 billion years ago. They also introduced electricity to mimic lightning, resulting in the production of amino acids, which are the fundamental building blocks of proteins. What somewhat weakens my confidence in this experiment is that not all amino acids are created equal. While glycine was indeed produced in the experiment, it happens to be the simplest amino acid in terms of its structural composition compared to the rest. Its chemical structure is shown below for reference:

It's quite easy to see how related this molecule is to ammonia for example coupled with methane. I suppose an answer to your question about why certain molecules are more prevalent than others, we can explore hydrocarbons. As the name implies, hydrocarbons consist of carbon-hydrogen (C-H) bonds. In general, due to carbon's unique atomic ability to form stable covalent bonds, hydrocarbons in turn are very stable molecules and common amongst all living things. Variations in the arrangement of carbon atoms in hydrocarbons give rise to different organic compounds, and hence they are selected for in nature. Thus, all roads eventually lead back to this statement I made earlier:
Molecules are favored due to the properties of the elements that compose them.