Many search engine marketers think who you link out to (and who links to you) helps determine a topical community of sites in any field or a hub of authority. Quite simply, you want to be in that hub, at the centre if possible (however unlikely), but at least in it. I like to think of this one as a good thing to remember in the future as search engines get even better at determining topical relevancy of pages, but I have never actually seen any granular ranking benefit (for the page in question) from linking out.
Advertising with Google won't have any effect on your site's presence in our search results. Google never accepts money to include or rank sites in our search results, and it costs nothing to appear in our organic search results. Free resources such as Search Console, the official Webmaster Central blog, and our discussion forum can provide you with a great deal of information about how to optimize your site for organic search.