Thinking of a new venture (either startup or a new initiative within a larger company), I would always suggest being focused on a single offering first, but with the following caveats:

1. In my view, the purpose of the first offering is to test the business hypothesis, this means not only offering but: target audience, need, specifics of the offering as the solution, and its differentiation. Really be laser-focused on all of these.
2. The only way to test that complete hypothesis is to develop, in full, an offering for a well-defined target audience, etc.
3. Once it is out and you measure adoption and success, it's critical to assess which of the assumptions are proven to be valid - could be that the need is not strong for this audience, or that there's not enough differentiation - the offering is only a part of it. You can only test this well if you developed a good offering to a well-defined audience solving a well-defined problem.
4. Then - iterate. You may need to change your offering, but you may also discover that your audience has a stronger need (they all email you and ask for it). The key here is "drop" everything and be flexible - now it is time to lose the former focus - you may need to make dramatic changes.

In my experience, companies that went through this cycle (of building a deep offering and then iterating based on the data it provides) have been the most successful.