The methodology to correctly identify the high-bandwidth devices that are able to deliver the lowest noise voltage-amplification from receiving terahertz antenna or photodiode current sources is detailed. We further show that to achieve the lowest noise levels, amplifier input capacitance must be minimized requiring the amplifier and detection circuitry to be carefully integrated. We validate a useful technique to minimize feedback parasitic capacitance and demonstrate a transimpedance amplifier (TIA) with a peak gain of 100 MΩ, 0.5 MHz bandwidth, and a signal power to noise power ratio (SNR) of 23 dB for a 5 nA peak-current input and outline the steps required to increase this to 50 dB. Employing this TIA on a 1550 nm fiber-based terahertz asynchronous optical sampling system realizes a 700 mV, 26 dB SNR, single-scan signal from the 8 nA peak/peak antenna source and removes the requirement for an additional data acquisition trigger signal. Real time, subsecond terahertz data collection is possible at a SNR of 30 dB averaging over 16 scans.