Every site is different and each keyword that you promote the site for will require a different amount of time and effort.
Non-competitive terms take less time to rank well than the more competitive terms. We would always recommend the use of a combination of both when promoting a site in the organic search engines.
In this way you get a quicker boost in visitor numbers from the less competitive terms and the more competitive terms follow on. This also gives you a base of credibility in the search engines as they will regard your site as more rounded and therefore a more likely source of reliable and helpful information for your visitors.