What measures of the dielectric constant mark whether the solution is ionic, polar and nonpolar? At what numerical values of ε, then what organic compounds if any mark these thresholds.  How is that only for a vacuum has ε=1?  This is absolute lowest limit?
Just compare the dielectric constant of known substances to non-polar, polar, metallic designations. For example, the dielectric constant of water is around 80.0 and water is polar. H2 has a very low constant value near 2 I believe and it is very non-polar. Metals have very large epsilon values moreover.  Rule of thumb, the larger the dielectric constant, the more polar the substance or material. In math terms, the potential felt between 2 charges is V= (q1 q2) / (4pi epsilon r) where q1 and q2 are different charges separated by r. The higher epsilon, the smaller V becomes. How charges interact with each other hence depends on the dielectric constant of the medium or material.