born2run... what you really want to happen from your site is to Share your story to Facebook, using the options their Open Graph protocol provides for. Sharing from your site, IMO, is much more important than Liking from your site... and I'm seeing remote Like used much less than remote Share.
Facebook Open Graph (og) meta tags on the pages in your site's head section provide reasonably thorough control of the display on Facebook: the story, the url, the headline, the description, and the image; and the FB location... and I think they are an important part of setting up a page to interface with your Facebook audience. IMO, selection of the images and headline are an important part of whether the shared post will attract attention.
But, again, the Like button on your site is less important than the Share button on your site. As I know we've discussed on other threads on this same topic, it's best to host any remote Share and Like buttons on your own pages, and to choose the varieties which are fast and efficient with bandwidth. We've easily had 4 or 5 discussions with you on the topic, with specific recommendations.
As robzilla suggests, there's no one right answer. The importance of remote Likes will differ depending on story and audience.
Also... from FB's algorithmic point of view, the stories that will get the most traction on the time line are stories which attraction comments from your friends... and Likes by themselves are less important than they used to be in getting Facebook to give your stories exposure.