This paper introduces the concept of spatial and media-based modulated (SMBM) orthogonal frequency division multiplexing (OFDM) as a potential candidate for highly mobile next generation beyond 5G (B5G) wireless communications. The proposed SMBM-OFDM technique utilizes not only the transmit antenna and channel state indices but also OFDM subcarriers to improve the system performance under high mobility. In addition, this study sheds light on challenging fast time-varying channel estimation problem of MBM-based systems by using the linear minimum mean square error (LMMSE) approach due to its optimality to investigate the achievable system performance with the aid of basis expansion modeling. The minimum lower bound on the channel estimation error (Bayesian Cramer-Rao bound) is derived theoretically and shown to be attainable by the considered LMMSE estimator. Moreover, symbol detection performance is provided for different modulation types and higher mobile velocities. Simulation results demonstrate that SMBM-OFDM system under high mobility is able to provide around 12-dB performance gains in terms of both channel estimation and symbol detection error compared to conventional spatial modulation (SM)-OFDM systems without MBM. The presented framework is important due to addressing the high mobility support of SMBM-OFDM systems for B5G wireless communications in terms of achievable channel estimation and data detection performance.