I don't think it will depend on competition for just choosing the keywords.
Keyword research process is going to be similar for most of the keywords. The thing is that doing SEO also OnPage SEO in competitive keywords scenario is a bit tougher. You have to watch out for keyword weights. It should not be less so that your competitors are on top of you. Plus it should not be much more so that search engines will see that you are spamming the index.
Offpage things remains as usual like link building and directory submission along with article submissions and Press releases.