What motivated him?
He didn’t do anything to standardize Catholicism. The only influence he had on the Church, aside from material things like donated churches and civil law, was that he requested an ecumenical council to settle the matter of Trinitarianism vs. Arianism. Not because he particularly cared either way (he enforced the ruling of Nicaea, but on his deathbed was baptized by an Arian), but because it was causing some political disruptions in Alexandria (then one of the most prosperous regions in the Roman Empire).
He also didn’t make Christianity the state religion of the Roman Empire, as is commonly assumed. That task fell to his successor Theodosius I in 380.
Constantine actually was a firm promoter of religious liberty, for those outside the faith that is.
What kind of historiographical approach should we take? In other words, what methodology to our study of history should we resort to? What assumptions about history shoukd we make?
What makes you think he did that? You must have something behind the question.
And I’ll raise you
The subject of the initial inquirey is so vast that it is beyond the scope of any internet site to accomodate a reasonable complete answer. Not only have innumerable University Term Papers, Masters Theses, and Doctoral Dissertations have been written on the subjects, there have been numerous text books written about Constantine and his relation with the Church.
As for what methodology should be used to study history, I side with the traditional methodology; the reason being, that any other methodology leads to false interpretations of historical facts and events in order to justify a particular political belief.
Like it or not, facts are facts and any interpretation of facts is conjecture, pure and simple.
Anything other than an honest statement of historical fact is nothing more than high class bovine excretment.
I think to say that he demanded the standardisation of the Catholic faith would be a bit of an overstatement. I do not think he was too concerned which way the faith goes but his priority is the civil unity of the Empire. So, he concern was that any split in the church could damage that civil unity. He was an emperor, after all.