To be blunt, I *HATE* FB.
I hate the psychologically manipulative way they acquire private information from people, particularly, kids.
I hate the way they completely ignore requests from photographers, both pro and amateur to allow some higher quality options instead of compressing the living daylights out of images, particularly, the reds.
I hate the way that they make ordinary users think they are FB's customers, when in actuality, FB's real customers are the firms who advertise using FB.
... and, so on, all the way down to the level of things like them refusing to remove the dark mask at the bottom of cover images, and making that mask even darker on their iPhone app. It completely ruins carefully crafted pix.
Unfortunately, I am forced to deal with FB because of one of my clients.
OK ... now that I got that off my chest, for ordinary pictures that you post (ie, not cover photos, not your profile photo), my recommendation is that you upload the largest pixel dimensions that they will accept, and make sure the "High Quality" box is checked. I did some checking and testing a couple of years ago, and tried some of the recommendations you'll see on the web (eg, upload only PNGs, upload nothing larger than 2048 px, etc.). I found no difference when following any of the usual recommendations. YMMV.
Tom M