The notion of ‘supposition’ (or rather its modern equivalents denotation, connotation, reference, meaning) is now treated in most Philosophy Departments under the rubric of Philosophy of Language and in that dispensation, is no less controversial than it was for the medievals. The subject is enormously complex and controversial and no two thinkers treat it in exactly the same way. The account in McCall is (necessarily) simplified and streamlined. (Apart from material, real and logical supposition, other thinkers discuss absolute and personal supposition!)
All that being said, the distinction between material supposition and all other kinds is pretty obvious. The problems arise in trying to distinguish between real supposition and logical supposition. One test is to ask yourself whether the predicate in a proposition can apply to the particulars that lie under a subject. If it can, then the supposition of the subject term is likely to be real rather than logical.
Your question pertains to a proposition such as ‘Justice is a virtue’ and here, the test doesn’t yield an obvious solution. It seems odd to think of their being particular justices but, if there were any such, they would each be virtues. That being so, the supposition here is real rather than logical.
Maritain’s book doesn’t cover informal logic.
Most handbooks on logic contain little more than you find in McCall. If you really want to investigate this topic, you need to go to specialist texts or back to the originals. In terms of drawing a contrast between logic as it was traditionally conceived and modern logic, Maritain’s book is good but the book that specifically deals with the topic is Henry Veatch’s Two Logics.
Let me give you a specific example of how the two logics differ.
In classical logic, the relationships on the square of opposition all hold completely independently of whether or not the terms in the propositions actually refer to anything in reality or not. The logical relationships are, as it were, meaning relationships, and questions of existence are not relevant..
In modern logic, only contradiction on the square of opposition holds. The reason for this is that for this logic, universal propositions are taken hypothetically and, as such, are deemed to be true even if the antecedent clause of the conditional is false! So, ‘All unicorns are wonderful’ would, for modern logic, be a true proposition. Bu the subordinate proposition, ‘Some unicorns are wonderful’ wold not be true unless there were in fact unicorns. So, for modern logic, the universal could be true but the subordinate proposition false.
For classical logic, however, the question of existence doesn’t arise here.
This has been a long response to a short question and may give you more headaches than it cures. The topics you are raising are important and controversial but with respect to gaining a facility in the formal side of logic, they are not completely relevant.