This paper presents optical long-slit spectroscopic observations of 105 barred Markarian IRAS galaxies. These observations are used to determine the spectral type (starburst or Seyfert) of emission-line regions in the nucleus and along the bar of the galaxies, in order to define a homogeneous sample of Starburst Nucleus Galaxies (SBNGs). Our selection criteria (ultraviolet excess, far infrared emission and barred morphology) have been very efficient for selecting star-forming galaxies, since our sample of 221 emission-line regions includes 82% nuclear or extranuclear starbursts. The contamination by Seyferts is low (9%). The remaining galaxies (9%) are objects with ambiguous classification (HII or LINER). The dust content and H{alpha} luminosity increase towards the nuclei of the galaxies. No significant variation of the electron density is found between nuclear and bar HII regions. However, the mean H{alpha} luminosity and electron density in the bar are higher than in typical disk HII regions. We investigate different mechanisms for explaining the excess of nitrogen emission observed in our starburst nuclei. There is no evidence for the presence of a weak hidden active galactic nucleus in our starburst galaxies. The cause of this excess is probably a selective enrichment of nitrogen in the nuclei of the galaxies, following a succession of short and intense bursts of star formation. Our sample of SBNGs, located at a mean redshift of 0.015, has moderate H{alpha} (10^41^erg/s) and far infrared (10^10^L{sun}) luminosities. The types are distributed equally among early- and late-type giant spirals with a slight preference for Sbc/Sc types because of their barred morphology. The majority (62%) of SBNGs are isolated with no sign of gravitational interaction. In terms of distance, luminosity and level of interaction, SBNGs are intermediate between HII galaxies and luminous infrared galaxies.