I don't share anything on Facebook because I feel like a big ol spammer when I do. It's all up to the individual, and you have to use your judgement about what you think your Facebook friends would like to see in their feeds. If you're active in a certain niche, or if you have a lot of friends and family you think would like to read and share your work without being annoyed, go ahead and post your work regularly. You can use your personal account, or you can start a page. It's up to you. You don't need a special business account, and pages are free and easy to create.
Even though I don't post my own work, I get plenty of visits from FB. If you get decent search traffic the kind folks of the internet will like your work and spread it around it all by themselves. You don't need to post on FB yourself to benefit from it.