Chest radiography is a medical imaging modality widely used in computer-aided detection (CADe) and computer-aided diagnosis (CADx) systems to detect and diagnose pulmonary diseases. Chest radiographs (CRs) are susceptible to unforeseen variations that could lead a CADe/CADx (CAD) system to fail. We propose a solution to this problem by analyzing multiple methods including two new methods, No-skip U-Net (NSU-Net-X) and Eigen-X, for CRs. Each method's performance is measured for three classification tasks: classification between lung images and not-lung images, identifying color-inverted CRs, and detecting rotated CRs. The NSU-Net-X, which is an adaptation of U-Net, shows an average performance of 0.99 for the three tasks. The Eigen-X approach, built similar to a widely used face detection method, shows a 0.98 average performance. Following the image screening algorithm, we propose applying lung segmentation on CRs due to its important role in computer-aided detection and diagnosis using CRs. Currently, the U-Net and DeepLabv3+ convolutional neural network architectures are widely used to perform CR lung segmentation. To boost performance, ensemble methods are often used, whereby probability map outputs from several networks operating on the same input image are averaged. However, not all networks perform adequately for any specific patient image, even if the average network performance is good. To address this, we present a novel multi-network ensemble method that employs a selector network. The selector network evaluates the segmentation outputs from several networks; on a case-by-case basis, it selects which outputs are fused to form the final segmentation for that patient. Our candidate lung segmentation networks include U-Net, with five different encoder depths, and DeepLabv3+, with two different backbone networks (ResNet50 and ResNet18). Our selector network is a ResNet18 image classifier. We perform training of the segmentation networks and the selector network using the publicly available Shenzhen CR dataset. Performance testing is carried out with two independent publicly available CR datasets, namely, Montgomery County (MC) and Japanese Society of Radiological Technology (JSRT). Intersection-over-Union scores for the proposed selector ensemble approach are 13% higher than the standard averaging ensemble method on MC and 5% better on JSRT.