Normally, I'd suggest a VNA to do these measurements since it'll tell you the mismatch of the amplifier (S11 and S22), but it maybe difficult with the MiniVNA as it looks like it has fixed output power, and in your case that power level could overpower your LNA (does it have a maximum input power specified?).
You will need to add an attenuator to reduce the power level at the input of your LNA so that you're working at the proper power level. S21 is the gain of the amplifer, exactly the figure you want. With the attenuator, your S11 measurement accuracy will be greatly degraded. Note that S21 is the voltage gain, assuming 50-ohm ports on the input and output. If your antenna or receiver are not exactly 50 ohms, the gain will be somewhat different in its final application.
If you go the oscilloscope route, I suggest having it measure "V_RMS cycle-to-cycle" when in AC coupling mode, and not Vpp. Vpp is much more influenced by noise in the oscilloscope. Also note that the siggen's output will be different amplitudes at different frequencies (especially towards its high end). You'll want to measure your THRU standard's V_rms at every frequency you'll measure. The oscilloscope's ADC is 8-bit, so you'll need to switch ranges to get a good measurement with and without the amplifier. Switching ranges will add a percent or two of inaccuracy in the gain. With the VNA, you would not need to change ranges, allowing you to make a more accurate gain measurement. At your frequencies, an external feedthru termination is fine, and the input capacitance of the oscilloscope is negligible.
As KG4ARN said, keep way below your P1dB. Going towards it will hurt your LNA's linearity (among other things).
PS: With fancier VNA's, testset ports are broken out so that the attenuator can be added on the VNA side of the coupler, allowing for better measurement accuracy. The couplers normally can handle more power than the receivers.