Absolutely post a link to your fundraiser page on your Facebook page. Regarding email - I say go for emails to friends who you email with at least occasionally.
Now in some cases, I would restrict the emailing further. For the organization you mention, I don't think it would be an issue. However, in situations where the fundraising is for or against something that people are for or against, e.g. political, reproductive issues, gun stuff, then I would only email those who I know had the same belief about the organization that I have.