It seems to me that atheism, like theism, is in and of itself a belief rather than a belief system — though, like theism, atheism is personal, subjective, and spectral, which is why both labels mean different things to different people.
For example, I personally believe there is no God. This doesn’t mean I’m certain about it: beliefs are, by definition, unprovable. (Otherwise, they’d be facts, in which case faith — i.e., personal commitment to belief — would be gratuitous.) It also doesn’t mean I'm antitheistic. I respect and support religion, since it provides significant benefits such as hope, comfort, strength, belonging, and structure to billions of people. The only thing I’m "anti" about is disrespecting each others’ personal, spiritual, existential boundaries.
Regarding belief vis-à-vis belief system as they apply to atheism (or theism), I believe beliefs beget belief systems. Here, too, I can reference experience: Once I admitted/accepted my belief, I recognized the need for a moral compass — a set of primary values to govern behavior, facilitate growth, and assist in considering conflicts. Then, I realized the need to base those values on what I care about most of all in life: how people treat each other. So I chose the principal values of equality, respect, understanding, and coexistence. They work well together in guiding me through life; thus, at least in my case, the belief, supporting values, corresponding worldview, and resulting behavioral code constitute a belief system.
Then again, "belief system" also means different things to different people: e.g., whether or not it involves a group rather than an individual; whether it’s formally codified; etc.
Please note that, as I see it, neither atheism nor theism is a moral position. One can embrace either belief and, independently, choose one’s personal moral code. (In contrast, "morality" implies a much higher degree of subjectivity, encompassing both one’s own perception and others’ perceptions, any or all of which may irreconcilably disagree.)
As to secularism and materialism, I’m not sufficiently knowledgable to discuss either term.