Can I build links and not submit the site to google after building a good number of links in maybe 1 month. I will submit it. Is that just OK?
That is perfectly ok, many infact will advise that you dont even need to submit to google, gaining backlinks from directories, sig links etc will get your site found naturally.
Unless you disallow all robots on your site, eventually getting all those links will get your site on google.
Preferally use the keyword you are targetting as the backlink. If you want to rank for "Cheap blue widgets", have your links be like this: Cheap Blue Widgets Although even a link like this: www.google.com can help you rank, it is better to have it be something like this: Cheap Blue Widgets