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As to your topic directly, you should not have to submit to any search engine, as long as someone else who is indexed finds you and links to your site. Submitting in and of itself doesn't hurt though.
Well the question is... which others?
The ongoing consolidation of search engine databases has brought a near-complete devaluation of submission services and software, and submission itself. The few remaining "major" search engines are likely to spider and add you before they'll do so in response to your url submission. The only significant reason to consider submission now is to get into more obscure minor search engines and directories and, depending on your industry, any applicable vertical directories or similar resources.
If you're considering submission services or software, you'd want to make sure that they cover any of those for your industry -- and you'd want to check whether automated url submissions will even work with the places you're targeting. But the bottom line is that automated submission today is pretty much dead -- which is why this forum [webmasterworld.com] has been deprecated for more than a year.
You will also discover that some keywords deliver more traffic then others. It is critical that you find the keywords and key phrases that people actually use in the SE’s.
Read the posts in Webmasterworld, learn to pick the right SE’s and learn to pick the right keywords and you will multiply your traffic quickly and if you learn good you will also be able to convert the traffic to sales