For certain commemorations of saints and also for certain feasts, there are two sets of Vespers: Small and Great. The texts differ as do the number of stichera at both "Lord I have Cried" and the Aposticha. Why is this? Is one celebrated earlier in the day as opposed to the other? Are great Vespers used as part of a vigil-rank feast/commemoration? I'd appreciate clarification.
Also, is it right that at any Great Vespers (3rd class or higher) that the psalter reading should always begin with the first Kathisma (Blessed is the Man)?
I'm going to echo GreekChef's answer and expand a bit.
Great Vespers is appropriate for certain feasts depending on the "size" of the feast (as you've observed a bit with your post). As the "size" increases, so too do the elements.
"Blessed is the Man" is only appropriate when it is called for by the Menaion. For example, St. Nicholas' feast day calls for "Blessed is the Man." However, it is not added
to the reading from the Psalter, but replaces it for that feastday.
Great Vespers is really only called "Great" when there is also a "Small" Vespers called for on the same feastday. As GreekChef pointed out, the only times when you see a double-vespers listed are on days when Vigils are done in Monasteries. The Small Vespers should occur at the normal time (before dinner, as she noted), while the Great Vespers will be left to "kick-off" the vigil.
So what makes a Vespers "Great" otherwise? Well, all Resurrectional Vespers are "Great", which means every Saturday evening, plus every Vespers of Bright Week (and Lazaros Saturday, which is a Resurrectional Day). Every Vespers of a "Despotiki" (Despotic/Lordly, referring to feasts of the Lord) or "Theomitoriki" (God Mother, referring to feasts of the Theotokos) Feast are Great. Vespers for Major Saints of the Church are also "Great" - of course, that depends on the local Church - as it should. But you can tell the "Great" commemorations from the hymns that are composed for them: If there are hymns for the Liti (procession of the Icon) in Vespers, if there are 4+ composed hymns for one saint for Lord I Have Cried; you can also tell by the presence of certain readings - Matins Gospel, Vespers Old Testament; and other elements, like the chanting of the Polyeleos or the "Blessed is the Man."
Finally, every Hierarchical Vespers is Great.