I suggest a mix of a SEO and non-SEO based plan. Let me tell you this upfront, to rank HIGH SEO competitive keywords to page 1, you may have to spend at least a thousand hours, or at least $1000 bucks, or both, to accomplish and sustain it. It's simpler and more high percentage to rank several related but lower comp terms, which together can better rank the site that is also using the broader niche term.
Meanwhile, you can do a non-SEO based (direct-link thru) campaign based on the high-comp keywords, by concentrating on promotion via viral videos, commenting on related highly ranked pages (be the links follow or no-follow), major sites (Yahoo Answers, Wikipedia, et al), and so on. This way you can get traffic based on the search engines for words you can rank high for, plus strong immediate traffic from direct links that stress the high comp keywords anyway. If you have a few hundred direct links from quality, highly-trafficked targeted sources, you won't need Google to benefit from a popular keyword.