DirectX is a low-level graphics API, similar to OpenGL. It's not a game engine or anything alike. It can be a good choice if you want to understand what happens behind the scenes, or forcefully write yet another engine (don't). However, it's definitely not the best option if you want quick results and well-abstracted production code. Nowadays, DirectX is hardly used directly for AAA games anymore, the big players either use a third-party commercial engine or write their own.
For independent development (to which you belong, unless you're part of a huge company), it depends on what your goals are. What kind of games do you aim for? Is your plan to develop a game without wasting any time, or do you want to learn plenty of details about game development and graphics programming? And last but not least, what resources (time, skill, people) do you have at hand?