Chest radiographs are among the most frequently acquired images in radiology and are often the subject of computer vision research. However, most of the models used to classify chest radiographs are derived from openly available deep neural networks, trained on large image-datasets. These datasets routinely differ from chest radiographs in that they are mostly color images and contain several possible image classes, while radiographs are greyscale images and often only contain fewer image classes. Therefore, very deep neural networks, which can represent more complex relationships in image-features, might not be required for the comparatively simpler task of classifying grayscale chest radiographs. We compared fifteen different architectures of artificial neural networks regarding training-time and performance on the openly available CheXpert dataset to identify the most suitable models for deep learning tasks on chest radiographs. We could show, that smaller networks such as ResNet-34, AlexNet or VGG-16 have the potential to classify chest radiographs as precisely as deeper neural networks such as DenseNet-201 or ResNet-151, while being less computationally demanding.