SMALL FILES: export images in low quality or export in high quality and compress?

It depends on many things. Option 1 doesn’t seem to be a good option if your first sentence says a goal is “better image quality.” Option 2 can be good if you find a website that can produce either higher quality files at the same file size, or same quality files at a lower file size. There have been reports that some of those websites can achieve a better balance than Lightroom Classic, but I have not tried them, so you have to run tests using your own images.

If this is for a web site, one JPEG technique I have read about for web sites is exporting at larger pixel dimensions at lower quality, and then scaling it down on the web page. For example if you need a 300 × 300 pixel image on a web page, try exporting it as 900 × 900 px image at a lower Quality setting and then use code on the web page to display it at 300 × 300 px, and that is said to look the same or better with a smaller file size. But again, you should test this with your own images to see if it is actually better.

Why don't you simply try 1 and 2 yourself and decide? You must be the judge anyway. A third option could be to export as tiff and then use another app to convert the tiff to jpeg, but I highly doubt this is all worth the trouble.

It would help if you defined what you mean by "small files".

Small files, by definition, will not have as good quality as the original.

I would imagine that the best way to have small files while losing as little as possible quality is to resize the image when exporting, while keeping the Quality slider at 70 or above.