(Rather than edit, I'm making a new post.)
In Classification of Closed, Locally Symmetric Spaces of Dimension $n$ and Rank $k$?, I asked about closed, locally symmetric spaces. I now realize what I really meant to ask about were simply-connected symmetric spaces (the universal covers of closed, locally symmetric spaces).
So, having read the referenced question, is there a classification by rank of simply-connected symmetric spaces of dimension $n$? To ask the same thing slightly differently, in relation to Helgason's classification of symmetric spaces in Differential Geometry, Lie Groups, and Symmetric Spaces by dimension, is there a (convenient?) way to arrange them in a given dimension by rank? [I'm new to symmetric spaces; do people simply think of them as "rank 1", "rank $n$", and "higher rank (excluding rank $n$?)"? There might be theorems that are true only for, say, rank 3 symmetric spaces in a given dimension $n \ge 5$.]