As keywords define each page of your site, you can use them to organize your content and formulate a strategy. The most basic way to do this is to start a spreadsheet (your "content to keyword map") and identify your primary keyword for each article. You can then build your sheet to your own requirements, add keyword search volume, organic traffic, page authority and any other metrics that are important to your business.
Google will select the best title it wants for your search snippet – and it will take that information from multiple sources, NOT just your page title element. A small title is often appended with more information about the domain. Sometimes, if Google is confident in the BRAND name, it will replace it with that (often adding it to the beginning of your title with a colon, or sometimes appending the end of your snippet title with the actual domain address the page belongs to).
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.