You will need a pulse amplifier. The order will go pulse generator->pulse amplifier->tee junction: -one tee junction output will go to the probe -one tee junction output will go to: preamplifier->console

You will need components between the probe, amplifier, and preamplifier to prevent the high power pulse from frying the preamplifier. Exactly how much power the pulse amplifier should put out depends on the quality of your probe (higher quality parts, solders, and design = more power before arcing occurs), but the amp should be capable of about 60 dB of gain. Maybe you could get away with 50 dB, maybe not.

The preamp brings the nanovolt signal up to a level that the console can work with, then the signal goes to the console and goes through two heterodyne detectors (lock-in amplifiers) arranged in a quadrature phase detection scheme. This allows phase-sensitive detection. The output from the console is then fed into a digital signal processor unit, which sends the digitized FID signal to a computer for software analysis and manipulation (Fourier transformation, apodization, zero filling, etc).

The fact that you asked whether or not the coil should be resonant with a capacitor suggests that you know far too little about electronic hardware to take this project on. But if you insist, then I've given you enough information to get started. Unless you already have a suitable pulse amp, preamp, and console/DSP/software setup, this could easily take you a year or more to complete. Simply designing and building a good probe could take a month or two. Your components will have to be high quality, I suspect, in order to detect such weak signals that would occur at 500 KHz, but I could be wrong.

There are a few good NMR hardware books out there. I'd start at the library and try to find them, or talk to a grad student who knows NMR technology for some recommendations. If I get a chance I'll update with some resource recommendations of my own.