We employ the self-consistent-charge density-functional tight-binding (SCC-DFTB) method for computing geometric, electronic, and vibrational properties for various topological isomers of small fullerenes. We consider all 35 five- and six-member rings containing isomers of small fullerenes, C-20, C-24, C-26, C-28, C-30, C-32, C-34, and C-36, as first part of a larger effort to catalog CC distance distributions, valence CCC angle distributions, electronic densities of states (DOSs), vibrational densities of states (VDOSs), and infrared (IR) and Raman spectra for fullerenes C-20-C-180. Common features among the fullerenes are identified and properties characteristic for each specific fullerene isomer are discussed.