  We investigate spectral properties of limit-periodic Schr\"odinger operators
in $\ell^2(\Z)$. Our goal is to exhibit as rich a spectral picture as possible.
We regard limit-periodic potentials as generated by continuous sampling along
the orbits of a minimal translation of a procyclic group. This perspective was
first proposed by Avila and further exploited by the author, which allows one
to separate the base dynamics and the sampling function. Starting from this
point of view, we conclude that all the spectral types (i.e. purely absolutely
continuous, purely singular continuous, and pure point) can appear within the
class of limit-periodic Schr\"odinger operators. We furthermore answer
questions regarding how often a certain type of spectrum would occur and
discuss the corresponding Lyapunov exponent. In the regime of pure point
spectrum, we exhibit the first almost periodic examples that are uniformly
localized across the hull and the spectrum.
