Deep neural networks (DNNs) are now a central component of nearly all state-of-the-art speech recognition systems. Building neural network acoustic models requires several design decisions including network architecture, size, and training loss function. This paper offers an empirical investigation on which aspects of DNN acoustic model design are most important for speech recognition system performance. We report DNN classifier performance and final speech recognizer word error rates, and compare DNNs using several metrics to quantify factors influencing differences in task performance. Our first set of experiments use the standard Switchboard benchmark corpus, which contains approximately 300 hours of conversational telephone speech. We compare standard DNNs to convolutional networks, and present the first experiments using locally-connected, untied neural networks for acoustic modeling. We additionally build systems on a corpus of 2,100 hours of training data by combining the Switchboard and Fisher corpora. This larger corpus allows us to more thoroughly examine performance of large DNN models -- with up to ten times more parameters than those typically used in speech recognition systems. Our results suggest that a relatively simple DNN architecture and optimization technique produces strong results. These findings, along with previous work, help establish a set of best practices for building DNN hybrid speech recognition systems with maximum likelihood training. Our experiments in DNN optimization additionally serve as a case study for training DNNs with discriminative loss functions for speech tasks, as well as DNN classifiers more generally.