Marketing on social media takes time but it sure takes dubble the time if I need to post any status/photo/link on any site separately.
It is a good idea to link your Facebook page to your twitter account because there are people who follow twitter accounts rather than FB pages and you don't want to miss them. I follow facebook pages and sometimes also the twitter account of the same page because with my smartphone it is easier just scrolling all updates with tweetdeck.
He is how to link your FB page to your twitter account.
You can then choose what to publish on your twitter account: status, notes, videos, photo's etc.