  This is the second in a series of papers concerning a new sample of low
luminosity compact (LLC) objects. Here we discuss the optical properties of the
sample based on Sloan Digital Sky Survey (SDSS) images and spectra. We have
generated different diagnostic diagrams and classified the sources as high and
low excitation galaxies (HEG and LEG, respectively). We have studied the
jet-host interactions, relation between radio and optical line emission and
evolution of the radio source within a larger sample that included also the
published samples of compact steep spectrum (CSS), gigahertz peaked spectrum
(GPS) sources and FRII and FRI objects. The optical and radio properties of the
LLC sample are in general consistent with brighter CSS and large-scale radio
sources, although the LLC objects have lower values of [OIII] luminosity than
the more powerful CSS sources (L_1.4GHz>10^25 W/Hz). However, when LLC are
added to the other samples, HEG and LEG seem to follow independent, parallel
evolutionary tracks. Regarding ionization mechanisms, LLC and luminous CSS
objects behave like FRII sources, while FRI seem to belong to a different group
of objects. Based on our results, we propose the independent, parallel
evolutionary tracks for HEG and LEG sources, evolving from GPS - CSS - FR.
