Dear Friend climber.
I am FB. member for 3 years and put most Misc. Photos for my Friends around the world to see. Yes, I reduce the Size of the Photos down to 18 Inches ( Max. Size of the widest size at 72 DPI, and Les than 1MB. per Photo.)= Yes = JPG file too.
Yes, As every one in this world know, All the photos on FB. or internet/ Web site can be copy and reuse any times with out notify the Owners/ Photographers----Ha, Ha, Ha.
Sorry to tell you that, That are the Truth in this world-----But When I see my Photos around the world in some magazine, I am very proud of my self = make me a very happy man.
I think climber was asking for tips on the best quality he could achieve on FB with his photos, rather than asking for people to toot their own horns with their photographic "accomplishments".
Regarding your question, it's been a difficult journey, but after a lot of experimentation there is a process I go through now before posting photos to FB. First, there are a few sizes of photos which FB does not alter the image size, including 720 px wide, and 960 px wide. Therefore, I downsize everything in Photoshop to 960px wide, to avoid any additional image size alterations done by FB. I also click the high quality option. While it allows a photo up to 2048 px wide, I'm not comfortable posting that massive of a resolution on the internet, but I retain more quality in the photo.
In the past, I had heard that FB will compress any JPG over 100KB in size, and for 960px wide, the JPG quality setting was often at 60% or so. But through experimentation, I found no discernable difference with any of the numerous photographs I posted at both 100Kb and higher (such as 500Kb or 1Mb). I'm not saying there was no difference, but in either case, the end result looked identical.