The other day I was trying to upload some early images from my Spring Fashion shoot with Grey Rock Clothing Co. a couple of weeks back. (Extra tip: Don't have a photo shoot and then go on vacation the next day. The images will be all you think about working on. Trust me.)
It was not unknown to me that Facebook does a shite job of handling your images once you've uploaded them resulting in some quality loss, but before now it was never bad enough that I refused to upload the image and find a better way to do it.
Fellow photographer Wendy Shepherd kindly pointed me to this FStoppers article that answered my question of "How can I prep my photos for uploading to Facebook?" Like all other distribution methods (be it print, web or video), there are settings to follow that will optimize your photo for display.
The thrust of the article is in resizing your image to that "golden" resolution. In the past I would export my pictures at a width of 1500px for web. In fact, this still remains the recommended width for uploading to a Squarespace gallery. It appears Facebook favours images that are sized to 2048 px. If you image is a landscape-oriented shot, then your width should be set to 2048. If it's a portrait-oriented shot, set your height to 2048.
This way your image will appear with the least amount of quality loss. You can see the final upload of mine to Facebook and how it turned out.