We present a first-principles study of the electronic, magnetic, and transport properties of the topological insulator Bi2Te3 doped with Mn atoms in substitutional (MnBi) and interstitial van der Waals gap positions (Mni), which act as acceptors and donors, respectively. The effect of native BiTe-and TeBi-antisite defects and their influence on calculated electronic transport properties is also investigated. We have studied four models representing typical cases, namely, (i) Bi2Te3 with and without native defects, (ii) MnBi defects with and without native defects, (iii) the same, but for Mni defects, and (iv) the combined presence of MnBi and Mni. It has been found that lattice relaxations around MnBi defects play an important role for both magnetic and transport properties.The resistivity is strongly influenced by the amount of carriers, their type, and by the relative positions of the Mn-impurity energy levels and the Fermi energy. Our results suggest strategies to tune bulk resistivities, and also clarify the location of Mn atoms in samples. Calculations indicate that at least two of the considered defects have to be present simultaneously in order to explain the experimental observations, and the role of interstitials may be more important than expected.