Did you know that Facebook posts with links aren't given preference by Facebook's algorithms? Can you guess why? One of Facebook's main goals is to keep you on Facebook as long as they can. Therefore, they "punish" links because they get people away from Facebook.
Using this same logic, you shouldn't give Facebook your traffic right away. You want to keep people onto your website, keeping your "bounce rate" as low as possible. The bounce rate measures how many people leave your website after viewing the first page. Once people go to Facebook, they're probably going to be distracted away from your organization and onto other things. Your goal should be to keep them on your website as long as you can (or at least send them to a link that you do want them on). If you do want a link to Facebook, the best place for that is on your website's footer (or on a social media page, if you have one on your website).