The more variety you have in the types of post you create on Facebook, the better. So, you could stand a better chance of drawing in a bigger audience if you add some video content to your Facebook page. Videos are a good way to engage your audience and you can create reviews or tutorials focused on the products you want to promote via affiliate links.
Affiliate networks offer you access to multiple (and by multiple, we mean hundreds if not thousands) of individual affiliate programs. They basically work by simplifying the signup process - instead of applying to become an affiliate for a each product you want to promote, you simply apply to join the network and instantly have access to hundreds of different affiliate offers.