Submitting to search does nothing. Create a Google Webmaster Tools account and submit a sitemap.xml. Make sure your site is designed in a way that makes it easy for visitors and the Google bot to crawl through your site and find all pages. Like everyone else is saying get quality backlinks and use social to promote your content.
Google, Yahoo and bing are enough. As guys mentioned above, search engine crawler will crawl your site automatically.
As I Know, you can use freewebsubmission.com resources for SE submission, Is a really a good resource, In this resource, there are more then 40 Search Engine/Search Engine Directories. I'm also using this resource...