The self-consistent charge density-functional tight-binding (SCC-DFTB) method is employed for studying various molecular properties of small fullerenes: C28, C60, and C70. The computed bond distances, vibrational infrared and Raman spectra, vibrational densities of states, and electronic densities of states are compared with experiment (where available) and density-functional theory (DFT) calculations using various basis sets. The presented DFT benchmark calculations using the correlation-consistent polarized valence triple zeta basis set are at present the most extensive calculations on harmonic frequencies of these species. Possible limitations of the SCC-DFTB method for the prediction of molecular vibrational and optical properties are discussed. The presented results suggest that SCC-DFTB is a computationally feasible and reliable method for predicting vibrational and electronic properties of such carbon nanostructures comparable in accuracy with small to medium size basis set DFT calculations at the computational cost of standard semiempirical methods.