By my experience, getting backlinks is more important than submitting your site to the search engines or building a sitemap. You may submit or build a sitemap for a site with no backlinks and it will never get indexed. On the other hand, a site with many backlinks and without a sitemap or a manual submission to the search engines, will be indexed soon.
A good mix of "all of the above" is likely the best route to go. Also, keep in mind that getting too many backlinks too fast, or from places that have little if any relevance to your site is not good either.