You see, it's all about content. Little Google robots scour websites for great content. Sites with great content get ranked higher. Actually, there's a lot more to it than that, but the saying "Content is King" is very much true.
SEO settings - Yes
Site Submissions - Yes
Extra services to help increase rankings - There are options, but they're not free, and still won't guarantee you the #1 spot . . . because we have no control over search engines.
The best way to keep your website relevant to search engines? Content. Provide content, services, products, etc. that people want, need, or think they want and need. They click, read, and perhaps stay awhile, which makes Google and other search engines happy.
Content. Is. King.
Google My Business
If you have a physical office/store location/brick-and-mortar, make sure you get listed with Google My Business, and keep the information updated. Utilize their post option (like a temporary blog, but right on Google), keep images fresh and interesting, and encourage happy customers and clients to leave reviews. These all help!