I am trying to upload an image to a website which has a requirement of minimum 1600 pixels on the longest side and max 20MB file size ... When I go to upload though the image becomes blurry on their website. I have been exporting them and changing the dimensions in the "Resize to Fit box" to Long Edge at 1600 pixels and resolution at 300 per cm.
It may be that the website will accept 1600 pixels as a minimum, but it may not be quite large enough for best quality. Try uploading a larger size.
Also be sure that Image Quality is set to 85 or higher during export.
If you export the photos, then view them outside of Lightroom but before you upload them. If they don't appear blurry, then the problem is the web site display of the photos. I agree with Joe, that the next step would be to upload larger files, you can uncheck "Resize to Fit" and see if that helps.