There are two biodiversity indices used in ecology:
1. Shannon's index accounts for both abundance and evenness of the species present.
2. Simpson's diversity index is the proportion of species relative to the total number of species.
So you need to decide which of these you prefer.
Plant density is different and is the number of plants of a certain species in a particular area and is determined by counting the number of individual plants of a species in uniformly sized sample plots within a site.
Your question is not completely clear, but in general a good starting point would be to read a bunch of journal articles to see what approaches others have taken and why, and how they interpreted their findings. For diversity at least, there are many ways for measuring and no one or two measures will capture all the information available in your data. Tons have been written on the subject and the scientific literature is full of published studies. I assume the same is true for density studies, although that's not my area of expertise. The book, Measuring Biological Diversity, by Anne Magurran, would also be a valuable read if you have access through your library or are able to purchase a copy. It discusses the benefits/drawbacks for various approaches.