With a sensor output of 1 to 20 milliVolts, and the need for lowest possible random noise floor, using 10 ohms Rg and Rfeedback would be wise. Such use would require 2 milliamp from the opamp, and even low-power opamps provide that much Iout.
Normal opamps have short-circuit values of 10 to 50 milliAmps. To supply 300 milliAmps would require a large (discrete?) unity-gain buffer after the opamp.
I'd use 1Kohm or 10Kohm, as the other answers suggested. If the bandwidth is 1,000KHz, knowing the noise density of 10Kohm is 12 nanoVolts/rtHz, the output noise contributed by the resistors will be Av=2 * 12nV/sqrt(2) * sqrt(1e6)
or Vout noise = 2 * 9nV * 1000 = 1.8 microVolts RMs, across the bandwidth from
DC to 1MHz (assuming your opamp performs well up to 1MHz).
Here is a noise simulation, done in Signal Chain Explorer
I've edited the answer to display the Thermal Distortion when 10 ohms and 10 ohms (Av = +2) are used. The opamp has default 5volt VDD, and 2mA Iout with (5volts -0.04volts) across the opamp's output transistors produces 1uV of low frequency distortion, as the output transistors send their heat across the die to upset biasing conditions of the input differential-pair transistors.
At 1uV distortion with 40,000uV output, the Thermal Distortion is -92dB.
Problem with Thermal Distortion is it becomes Amplitude Modulation of all the
tonal content; any higher tones become tiny AM_radio signals with sidebands carrying the low-frequency signals.
To view the conditions for defining Thermal Distortion, click on the "thermal" tab on the opamp stage; you'll see the cause of opamp Thermal Distortion is change in Input Offset Voltage at 1uV/degreeC; you'll understand the reason for only low-frequency signals causing Thermal Distortion as the Thermal Resistance and the Thermal Capacitance (using specific-heat of silicon) define the die's thermal timeconstant (bandwidth of the die's thermal response), assuming an non-distributed-RC model.
By the way, the tool has "Gargoyles" mode. In top center, click Gargoyles on, then click UPDATE on right side. You've just activated magnetic field, electric field, power supply and ground_plane INTERFERERS. To view the active interferers of each type, click on the label: HFI/EFI/PSI/GPI.
Notice the SNR drops, perhaps significantly, when the trash-injectors, the Gargoyles, are enabled. The HFI interferer, by default a switch regulator with
dI/dT of 10MegaAmp/second current slewrate, couples into a 14mm by 1.5mm loop, which is the PCB trace between stages.
To view the interconnects, find and click "Show Interconnects" at top left. You can see the details of the PCB trace (the interconnect) between any two stages by clicking on the BLUE region between stages. Again, the default trace length is 14mm, on a 0.06" (1.5mm) double-sided PCB with GND.
To better understand what is happening, click "Analysis Details" on middle right.