A new methodology for finding the low-energy structures of transition metal clusters is developed. A two-step strategy of successive density functional tight binding (DFTB) and density functional theory (DFT) investigations is employed. The cluster configuration space is impartially searched for candidate ground-state structures using a new single-parent genetic algorithm [I. Rata , Phys. Rev. Lett. 85, 546 (2000)] combined with DFTB. Separate searches are conducted for different total spin states. The ten lowest energy structures for each spin state in DFTB are optimized further at a first-principles level in DFT, yielding the optimal structures and optimal spin states for the clusters. The methodology is applied to investigate the structures of Fe-4, Fe-7, Fe-10, and Fe-19 clusters. Our results demonstrate the applicability of DFTB as an efficient tool in generating the possible candidates for the ground state and higher energy structures of iron clusters. Trends in the physical properties of iron clusters are also studied by approximating the structures of iron clusters in the size range n=2-26 by Lennard-Jones-type structures. We find that the magnetic moment of the clusters remains in the vicinity of 3mu(B)/atom over this entire size range.