Interpreting echocardiographic exams requires substantial manual interaction as videos lack scan-plane information and have inconsistent image quality, ranging from clinically relevant to unrecognizable. Thus, a manual prerequisite step for analysis is to select the appropriate views that showcase both the target anatomy and optimal image quality. To automate this selection process, we present a method for automatic classification of routine views, recognition of unknown views, and quality assessment of detected views. We train a neural network for view classification and employ the logit activations from the neural network for unknown view recognition. Subsequently, we train a linear regression algorithm that uses feature embeddings from the neural network to predict view quality scores. We evaluate the method on a clinical test set of 2466 echocardiography videos with expert-annotated view labels and a subset of 438 videos with expert-rated view quality scores. A second observer annotated a subset of 894 videos, including all quality-rated videos. The proposed method achieved an accuracy of for the joint objective of routine view classification and unknown view recognition, whereas a second observer reached an accuracy of 87.6%. For view quality assessment, the method achieved a Spearman's rank correlation coefficient of 0.71, whereas a second observer reached a correlation coefficient of 0.62. The proposed method approaches expert-level performance, enabling fully automatic selection of the most appropriate views for manual or automatic downstream analysis.