Which niche you decide to target on your home page is up to you, but in general, the better user experience leans towards broader terms. You can focus deeper on internal pages, but be welcoming to a large crowd (an important, more general key phrase) on your homepage.
Why I say it's up to you, is because it's important to know the risk vs. reward, there is no definite answer. Going too broad will have you fighting against giants you can't yet compete with. Focusing too narrow will limit your demographic scope and traffic. As the SEO, it's up to you to do the research and discuss the levels of risk and reward with your client. What will take longer, what kind of results can they expect from each, etc.