  In this article, we present a classification for the divisor topologies of
the projective complete intersection Calabi-Yau (pCICY) 3-folds realized as
hypersurfaces in the product of complex projective spaces. There are 7890 such
pCICYs of which 7820 are favorable, and can be subsequently useful for
phenomenological purposes. To our surprise we find that the whole pCICY
database results in only 11 (so-called coordinate) divisors $(D)$ of distinct
topology and we classify those surfaces with their possible deformations inside
the pCICY 3-fold, which turn out to be satisfying $1 \leq h^{2,0}(D) \leq 7$.
We also present a classification of the so-called ample divisors for all the
favorable pCICYs which can be useful for fixing all the (saxionic) K\"ahler
moduli through a single non-perturbative term in the superpotential. We argue
that this relatively unexplored pCICY dataset equipped with the necessary model
building ingredients, can be used for a systematic search of physical vacua. To
illustrate this for model building in the context of type IIB CY orientifold
compactifications, we present moduli stabilization with some preliminary
analysis of searching possible vacua in simple models, as a template to be
adopted for analyzing models with a larger number of K\"ahler moduli.
