Metaphysical Possibility

As I've said in a previous post, I wonder (and in great ignorance, no doubt) what could confer support on the proposition possibly, God exists.

Edward Feser has an intriguing, short article on Plantinga's ontological argument in which he says,

"...a failed attempt to discover a contradiction in some concept itself provides at least some actual evidence to think the concept describes a real possibility"

The distinctions between logical, broadly logical and metaphysical possibility are quite confusing to me.  If a concept doesn't entail any contradictions, then this would surely imply (narrowly) logical possibility.  But what kind of conceptual analysis takes us further into broadly logical possibility?  William F. Vallicella often discusses this perplexing topic (on which he is has also written at length in published journals) on his blog, but I am still a bit fuzzy on these distinctions.