We propose a detailed description of the structural and electronic properties of neutral and charged TinO2n+m clusters (n=1-3 and m=0,1), through simulations based on the density functional theory in the local spin density approximation. In all the isomers studied, strongly bound titanyl groups are found. The order of stability of the low-energy stoichiometric clusters may change considerably from that found by the approaches based on classical electrostatics. The most stable isomers of the oxygen-rich neutral clusters show characteristic peroxide groups. All these facts stress the importance of the covalent contribution to the cohesion of the clusters. Large atomic relaxations, accompanying the change from a closed-shell to an open-shell electronic configuration when an electron is added or removed, can often induce reversals of stability among the isomers. A careful discussion of the computed electron affinities and excitation energies as a function of the size and the atomic conformation of the clusters is performed, in relation to recent experimental data.