Strobing does two things. It forces a time point at each strobe point and it suppresses the output of anything but the strobe points. It is a powerful concept that can be extremely useful in certain circumstances. If you strobe at the clock frequency, the clocks will seem to become constant because you are only sampling them once per period. Also clocked sine waves seem to become purely sinusoidal. In effect, any harmonic of the sample rate disappears from the displayed signal.
For accurate Fourier analysis, you need to place a strobe point under every Fourier analysis sample point. There is no need to place strobe points between the sample points. You would specify strobe period to get the strobe rate you want, and you would set skip start or strobe delay to adjust the phase of the strobing. This allows you to sample the circuit at just the right time (generally you want to sample at the end of the settling time for a clocked output).
You need the fundamental frequency of the signal being analyzed to be an exact multiple of the sample rate, and the multiple should equal the number of samples being used by the Fourier analysis. So for example, if your sample period is 10ns and your Fourier analysis is using 512 points, then the fundamental frequency should be 195,312.50 Hz. You should not use any windowing (which is equivalent to rectangular windowing).
In my experience people think the more points they use in the Fourier analysis, the more accurate the results. This is false if there is no significant aliasing, which there generally is not if the signal is sinusoidal or a sinusoid clocked at the Fourier analysis sample rate. Instead the use of a large number of points in the FFT just serves to make the simulation expensive. Similarly, it is not necessary to analyze multiple periods. Again, that just wastes simulation time.
However, allowing the signal to settle to eliminate initial transients is important. You should wait 10-20 time constants at least before starting the Fourier analysis depending on the desired accuracy. Thus, in general, you always want the Fourier analysis interval as late in the simulation interval as possible.
It is difficult to get all this right. One thing that you should do as a sanity check to find obvious problems is the also look at the computed spectrum of the input signal. If you are seeing any significant harmonic content, then something is not right.