Scientific papers (as well as commercial reports) usually contain the number of elements, nodes and sometimes also DOFs. This, in addition to screenshots of the mesh, gives readers the idea about the level of discretization and problem size.
Given the level of question you are asking, I highly recommend supervision from an expert. Computational tools, in inexperienced hands, can be a ticking time bomb. This is not to scare you; it is fantastic thing to play with computation - as long as you have an expert watching over you and nudging you in the right direction. While experts in public forums do the best they can in their spare time, they cannot come close to replacing feedback from someone in your team, especially at an early stage.
To your question, while the number of elements/nodes/DOFs .. is a good thing, what you really want to see is the ultimate quantities of interest being independent of the level of discretization in space and time. In other words, the result should be within an acceptable level of tolerance (i.e., not change by much) after some degree of refinement. Unfortunately, the rabbit hole goes deep so I will stop here.
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I think that for a scientific article you should generally provide the information required to make it possible for somebody to run the same analysis or something comparable. In that context I think that the number of elements and type of elements may be relevant information. For an article in a newspaper the number of elements used to analyze a new car probably doesn't mean much for the average reader .