So you're trying to look for necessary and sufficient conditions for metrizability? I know that every locally compact and locally connected normal Moore space is metrizable, but that is merely sufficient.
I would suggest looking in Jstor or "The Handbook of Set-Theoretic Topology". Maybe even ask the member Plato since he is very knowledgeable (his instructor actually may have been) R.L. Moore for which these spaces are named after.