There is no such thing as a "best" resolution, except for the original video's "native" resolution!
Generally it is highly recommended to
not resize at all. If you
do resize, you should know
why you need a resize. And then you also know what your target resolution is.
If you do not have a good reason to resize, then simply do
not resize
Be aware: Some applications use "bits per pixel" (aka "bpp") as a metric to predict the quality of the re-encoded video.
So maybe (I don't know, I just speculate) AutoGK will lower the resolution based on the target average bitrate (target file size) until a certain minimum "bits per pixel" value has been reached.
It should be obvious that using "bits per pixel" as a quality indicator is
complete nonsense, because it completely leaves out the "complexity" or "compressibility" of the individual video!
Having said that, in extreme cases, such as
ultra-low bitrate encodes, it may indeed make sense to downsize the video prior to encoding. Generally that's not the case though.