It really depends on what you want. Groups are good for attracting quick attention. They allow you to send out 'bulk invites" pages are usually better for a long term relationship with your customers...
If you are serious about Advertising on facebook for free, than I suggest that you use both ways. Depends on how many sites you will promote and how often. Remember that Facebook is a social media and therefore you have to be present often. Ask yourself if you have the time to do both groups and fan/like pages. If not then I suggest using fan pages because they have more potential! Regards
fan page is the best because there you have lot of options and more advanced than a group. Fan page has no limit of members as I know
Fan Page. You can customize it, you have more rights to it. I am experienced with making custom iFrame facebook fan pages. PM me if you are interested, I can make a reveal tab so that your users have to Like the page first, before they can see the content.