Circuit design: detecting oscillating magnetic fields with pick-up coil, amplifier, filter
up to where you estimated the voltage I understand what you do and it is correct.
Now, the 


  As such, we can set Vout=(1 V/μT)B and solve for the ratio of R1/R2 that solves properly calibrates the signal, no?


I don't understand what you mean by that. However, I think you're on the right track. 
You have $$V_{coil} = N\pi r^2 B_0$$ 
and you want $$ A\cdot N\pi r^2 B_0 = 1V$$ where \$A\$ is the amplification factor and \$B_0\$ is \$1\mu T\$ (sorry too lazy to solve this). Now as you have \$A\$, you can calculate \$R_1, R_2\$ by solving $$ A = (1+R_1/R_2)$$ (choose one value and solve for the other. You might want to use some values in the range of 1k to 1M Ohm). Lastly you put a bandpass filter in front of the opamp, composed of an RC lowpass and an RC highpass. 26k for both resistors and 100nF for both capacitors will do the job. 
See here: https://electronicbase.net/band-pass-filter-calculator/
or google for "opamp bandpass".