Constantine's chief aim, from what I understand, was to get the chruchmen to agree on a common doctrine, but he was less concerned as to what it was.  If Christianity was to be one of the official religions of the Empire, he did not want a lot of doctrinal squabbling.  I believe that the story of his vision of a cross and conversion was apocryphal and a later invention once the church had become The Church.

The rejection of the Arian beliefs and the adoption Nicaean Creed were the primary "accomplishments" of the Council and were related, but Constantine's two immediate successors were Arians and various pagan factions continued for years to seek to increase their influence.  The process of establishing caesaropapism may be considered to have begun at this council, but it was far from complete.  Constantinople would not be founded for another five years and the Byzantine Empire dates from 395, by which time it is safe to say that caesaropapism was well established.

"It is not necessary to have hope in order to persevere."