Andrea,
That's a fine idea. Likes for your Fan Page are always a good way to get promotion within Facebook as Pages with more likes will show up in their friends wall and 'Pages related to this area' more often. For Likes on your website pages, that can increase exposure through friends wall posts as well as any 3rd party sites that harvest like counts for websites to improve relevance (most notably bing.com).
With JFBConnect 3.4, you can easily show an article or whole page from your site using the Page Tab integration. In that article that's shown, you can simply use the {JFBCLike url=http://gothicengine.com} for a like to your home page as well as a {JFBCLike url=http://www.facebook.com/gothicengine} (assuming that's your page name) for the Page itself. The latter one will be in addition to the Like button at the top of every Fan Page.
On your main website, you can also use the same tags, or even the {JFBCFan url=http://www.facebook.com/gothicengine} to show a more feature rich Fan Page like button with your stream and profile pictures if you want.
Either way, using your Page or your website to promote the other is always a good idea
If you have any questions on how to do more, or need help, just let us know.
Thanks,
Alex