We propose several low-complexity transmit antenna selection (TAS) and precoding schemes for massive multi-input multi-output (M-MIMO). It is well established that large antenna arrays in M-MIMO lead to particularly high hardware overheads as they require an equally large number of radio-frequency chains, and antenna selection is envisaged as a solution to reducing this hardware complexity. Accordingly, in the proposed schemes, both hardware and computational complexity of M-MIMO systems are addressed by jointly optimizing TAS and precoding. We first introduce a mixed-integer programming approach that simultaneously identifies the transmitting antennas subset and solves the precoding problem, by employing a unified metric based on constructive interference (CI) concept. We then propose three sub-optimal techniques that allow a reduction of the computational complexity required to solve the joint optimization. Our analyses and results prove that the proposed joint TAS and precoding schemes based on CI exploitation are able to outperform the state-of-the-art, while providing a favorable performance-complexity tradeoff.