Currently, the diagnosis of Autism Spectrum Disorder (ASD) is dependent upon a subjective, time-consuming evaluation of behavioral tests by an expert clinician. Non-invasive functional MRI (fMRI) characterizes brain connectivity and may be used to inform diagnoses and democratize medicine. However, successful construction of predictive models, such as deep learning models, from fMRI requires addressing key choices about the model's architecture, including the number of layers and number of neurons per layer. Meanwhile, deriving functional connectivity (FC) features from fMRI requires choosing an atlas with an appropriate level of granularity. Once an accurate diagnostic model has been built, it is vital to determine which features are predictive of ASD and if similar features are learned across atlas granularity levels. Identifying new important features extends our understanding of the biological underpinnings of ASD, while identifying features that corroborate past findings and extend across atlas levels instills model confidence. To identify aptly suited architectural configurations, probability distributions of the configurations of high versus low performing models are compared. To determine the effect of atlas granularity, connectivity features are derived from atlases with 3 levels of granularity and important features are ranked with permutation feature importance. Results show the highest performing models use between 2-4 hidden layers and 16-64 neurons per layer, granularity dependent. Connectivity features identified as important across all 3 atlas granularity levels include FC to the supplementary motor gyrus and language association cortex, regions whose abnormal development are associated with deficits in social and sensory processing common in ASD. Importantly, the cerebellum, often not included in functional analyses, is also identified as a region whose abnormal connectivity is highly predictive of ASD. Results of this study identify important regions to include in future studies of ASD, help assist in the selection of network architectures, and help identify appropriate levels of granularity to facilitate the development of accurate diagnostic models of ASD.