We present a self-calibrating, SI-traceable broadband Rydberg atom-based radio-frequency (RF) electric (E) field probe (the Rydberg Field Probe or RFP) and measurement instrument (Rydberg Field Measurement System or RFMS). The RFMS comprises an atomic RF field probe (RFP), connected by a ruggedized fiber-optic patch cord to a portable mainframe control unit with a computer software interface for probe RF measurement and analysis including real-time field and measurement uncertainty readout, and spectral RF waveform visualisation. The instrument employs all-optical electromagnetically induced transparency (EIT) readout of spectral signatures from RFsensitive Rydberg states of an atomic vapor for self-calibrated, broadband measurements of continuous, pulsed, and modulated RF fields. The RFP exploits resonant and off-resonant Rydbergfield interactions to realize broadband RF E-field measurements at frequencies ranging from ∼10 MHz to sub-THz, over a wide electric-field dynamic range, with a single vapor-cell sensing element. The RFMS incorporates a RF-field-free atomic reference as well as a laser-frequency tracking unit to ensure RFMS reliability and accuracy of the RF E-field measurement. Atomic RF field measurement uncertainties reaching below 1% are demonstrated. We characterize the RFP and measure polar field patterns along primary axes of the RFP at 12.6 GHz RF, obtained by single-axis rotations of the RFP in the far-field of a standard gain horn antenna. Field pattern measurements at 2.5 GHz are also presented. The measured field patterns are in good agreement with finite-element simulations of the RFP. The data confirm that the atom-based RF E-field probe is well-suited for broadband isotropic RF measurement and reception. A calibration procedure and an uncertainty analysis are presented that account for deviations from perfectly isotropic response over 4π solid angle, which arise from asymmetric dielectric structures external to the active atomic measurement volume. The procedure includes contributions from both the fundamental atomic-spectroscopy measurement method and their associated analysis as well as uncertainty contributions due to material, geometry, and hardware design choices. The calibration procedure and uncertainty analysis yields a calibration (C) factor, used to establish absolute-standard SI-traceable calibration of the RFP. Polarization pattern measurements are also performed, demonstrating RF-polarization detection capability with the instrument that can optionally be implemented simultaneously with E-field measurements. RFP measurement capability for pulsed and modulated RF fields as well as direct, time-domain RFpulse waveform imaging are demonstrated. We conclude with a discussion of the practical use of the Rydberg atom-based RF E-field probe instrumentation in RF metrology towards the establishment of a new absolute (atomic) RF E-field measurement standard, application areas in RF measurement and engineering, and its value as a new quantum technology platform readily adaptable to spec...