There's really no point submitting your site to Google. It's a waste of time.
If the site has valid incoming links, the site will be spidered, in Google's own time, and your pages will be indexed (so long as there's no serious breach of the Guidelines).
Any benefit will not be instant, but once the site can be found on any search, it can be found on every search for every word that appears on the site.
But of course the page won't appear in the same place for every key word or phrase.
If you mention "antiquarian aardvarks", then that search is likely to produce a solid result, as relatively few such pages exist. If you mention 'real estate', a slightly more competitive term, your site may may feature rather lower - say a billion pages lower.
But it will be in there, fighting its corner!