We examine a representative sample of 35 Seyfert 2 nuclei. Previous work has shown that nearly half (15) of these nuclei show the direct (but difficult-to-detect) spectroscopic signature at optical/near-UV wavelengths of the hot massive stars that power circum-nuclear starbursts. In the present paper we examine a variety of more-easily-measured quantities for this sample, such as the equivalent widths of strong absorption features, continuum colors, emission-line equivalent widths, emission line ratios and profiles, far-IR luminosities, and near-UV surface brightness. We compare the composite starburst + Seyfert 2 nuclei to "pure" Seyfert 2 nuclei, Starburst galaxies and normal galactic nuclei. Our goals are to verify whether the easily-measured properties of the composite nuclei are consistent with the expected impact of a starburst, and to investigate alternative less-demanding methods to infer the presence of starbursts in Seyfert 2 nuclei, applicable to larger or more distant samples. We show that starbursts do indeed leave clear and easily quantifiable imprints on the near-UV to optical continuum and emission line properties of Seyfert 2's. Composite starburst + Seyfert 2 systems can be recognized by: (1) a strong "Featureless Continuum" (FC), which dilutes the CaII K line from old stars in the host's bulge to an equivalent width W K < 10Å; (2) emission lines whose equivalent widths are intermediate between Starburst galaxies and "pure" Seyfert 2's; (3) relatively low excitation line-ratios, which indicate that part of the gas ionization in these Seyfert 2's (typically ∼ 50% of Hβ) is due to photoionization by OB stars; (4) large far IR luminosities ( 10 10 L ); (5) High near-UV surface brightness (∼ 10 3 L pc −2 ). These characteristics are all consistent with the expected impact of circum-nuclear starbursts on the observed properties of Seyfert 2's. Furtheremore, they offer alternative empirical diagnostics of the presence of circum-nuclear starbursts from a few easily measured quantities.