The value of reading high-ranking journals in your field is that it will give you a somewhat broad view of what leading researchers in your field consider to be "good" and "important" research.
However, this "breadth-first" approach will not help you very much in your own research, including getting your own papers published.
Instead, I suggest you pursue a "depth-first" approach where you find "seminal" papers in the sub-fields that interest you the most, and then read all the important papers that cite those seminal papers, especially papers that argue against the seminal/foundational papers. In this way, you learn about the scientific discourse involved in any particular line of research.
You can find seminal papers several ways. Sometimes, they are highly cited. Other times, they are the focus of special issues of journals or special conferences. Sometimes, they aren't highly cited (i.e. do not have a high number of citations themselves), but they are cited or used in a few critical papers which in turn led to a significant line of research.
With this sort of analysis, you will learn the skill of evaluating papers not in isolation but in the context of a whole line of research, including research by detractors.
I advocate the "depth-first" approach to support your own research because in your dissertation you will need to take a position through your thesis statement(s) on a few research question(s). For this purpose, it is of little value to know all the latest research in the best journals. Instead, you need to know all (or most) of the research in one or a couple of lines of research, and especially the gaps in that research which you intend to fill with your dissertation.