You don't need more focal lengths. You may find that that 24mm fits your style perfectly. Its wide field of view is a traditional favorite, and it's never really gone out of style. The popular Fujifilm X100 comes with a similar non-interchangeable lens, and for that matter, it's about what you get from the iPhone's built-in camera.

You may like to have some versatility. The perspective compression given by a longer focal length is often seen as more flattering for portraits — with a wide angle lens you have to get right up close to fill the frame with a subject's face, and that can look odd. The links @dpollitt suggests in his comment up above offer good background into all of this, and I recommend reading them if you aren't clear on the concepts. But since you say you've researched focal length, maybe that's just fine with your style.

The common advice is to start with a cheap zoom, and it's not bad advice at all, but it's also just fine to take the less-travelled path if it appeals to you. Why waste your time mucking around, if you feel like this lens will fit what you want? If you get just the 24mm and work with that as your photography, you'll be better off than many photographers with arsenals of zooms and primes but no vision.