The problem you have is the mixture of terms that the contest organisers and yourself are using.
On the one hand they are asking for a high resolution file with a maximum file size of 20MB.
On the other, PhotoLab doesn’t have an export option explicitly for file size; the nearest you can get is Megapixels, but that can give you all sorts of file sizes depending on what quality you specify for the jpeg compression.
Let me take one of my files from a Nikon D810, 36 Megapixels where the RAW file is 79MB.
I export it at full size and 100% jpeg quality and get a jpeg file of 75MB. The resolution is marked as 72ppi but that is totally irrelevant because changing that will only change the physical printing size, not the size or quality on screen.
Next I export it at 80% jpeg quality and, this time, I get a jpeg file of just under 15MB; exporting at 90% gives me just over 22MB.
You asked what settings you would use to to create the highest quality jpeg, but then you ask what resolution to use. As I said, resolution is irrelevant unless you are wanting to print the image to a certain size - exporting at 300 ppi yields exactly the same file size as exporting at 72 ppi.
You don’t need to worry about interpolation unless you are reducing the pixel size of the image.
If I were you, unless your image is already smaller, I would enter a “longest edge” figure that gives you a 24Mpx image size (at 3:2 proportions, that would be 6000px). The resolution can be anything you want (most modern larger screens are around 110ppi; for printing you would set it to 240ppi). Then I would use bicubic interpolation if your original file is significantly larger or bilinear if it is already at or near 24Mpx. Finally, I would start at 100% jpeg quality and just keep on reducing that until the file size is smaller than 20MB.
I can’t think of any other way without losing control of the quality of the output, which you want to be the best possible within the given file size.