I would only recommend submitting once to Major SE's if your focus is mainly Google Traffic then a slight increase in Google crawl rate via Googles Web master tools is a good way to get any new content and pages crawled and indexed fast, It also helps for first timers to setup your site via web master tools to help inclusion in the SE quickly.
Submitting site multiple time to search engine will not actually increase your page rank, if you are talking about google.
So try to drop as many backlinks you can, it will drive site growth into a very positive mode. Try to use webmaster tools to check the broken links and your page impression.
Submit your sitemap using Google webmaster, that way Google will re-visit as per the parameters in your sitemap and Google's own notion about the site's modification frequency. Another advantage of sitemap is you can tell Google not to miss any important page.