Hi Kano:
Great decision in making a Facebook Page for your site. It’s an excellent way to get further exposure to your site. One of the best things about Facebook pages is that they’re public- so they’re not behind a FB login. This way Search Engines can index the page, and if people come across your site’s FB page in SERPs it can potentially result in more traffic to your site.
As for selecting the category for the page, it’s very important. As a suggestion, you can implement broad category targeting for your page and actually select multiple categories. This way you will not be narrowing the channel of results that can come through for your page.
Hope this info helps! Best of luck!