Wide bandwidth requirements for multi-Gbps communications have prompted the global telecommunications industry to consider new mid-band spectrum allocations in the 4--8 GHz FR1(C) and 7--24 GHz FR3 bands, above the crowded bands below 6 GHz. Allocations in the lower and upper mid-band aim to balance coverage and capacity, however, there is limited knowledge about the radio propagation characteristics in the 4--24 GHz frequency bands. Here we present the world's first comprehensive propagation measurement study at 6.75 GHz and 16.95 GHz in mid-band spectrum conducted at the NYU WIRELESS Research Center spanning distances from 11--97 m using 31 dBm EIRP transmit power with 15 and 20 dBi gain rotatable horn antennas at 6.75 GHz and 16.95 GHz, respectively. Analysis of the omnidirectional and directional propagation loss using the close-in free space model with 1 m reference distance reveals a familiar waveguiding effect in indoor environments for line-of-sight (LOS). Compared to mmWave frequencies, the omnidirectional LOS and non-LOS (NLOS) path loss exponents (PLE) are similar, when using a close-in 1 m free space path loss reference distance model. Observations of the omnidirectional and directional RMS delay spread (DS) at FR1(C) and FR3 as compared to mmWave and sub-THz frequencies indicate decreasing RMS DS as the carrier frequency is increased. The RMS angular spreads (AS) at 6.75 GHz are found to be wider compared to 16.95 GHz, showing greater number of multipath components from a broader set of directions in the azimuthal spatial plane when compared to higher frequencies. This work also presents results from extensive material penetration loss measurements at 6.75 GHz and 16.95 GHz using co and cross polarized antenna configurations for ten common construction materials found inside buildings and on building perimeters, including concrete walls, low-emissivity glass, wood, doors, drywall, and whiteboard. Our findings show penetration loss increases with frequency for all of the ten materials and partitions tested, and suggest revisions of 3GPP material penetration loss models for at least infrared reflective (IRR) glass and concrete may be necessary. The empirical data and resulting models for radio propagation and penetration presented in this paper provide critical information for future 5G and 6G wireless communications.