Recently, deep learning models have been widely spread in the industrial recommender systems and boosted the recommendation quality. Though having achieved remarkable success, the design of task-aware recommender systems usually requires manual feature engineering and architecture engineering from domain experts. To relieve those human efforts, we explore the potential of neural architecture search (NAS) and introduce AMEIR for Automatic behavior Modeling, interaction Exploration and multi-layer perceptron (MLP) Investigation in the Recommender system. The core contributions of AMEIR are the three-stage search space and the tailored three-step searching pipeline. Specifically, AMEIR divides the complete recommendation models into three stages of behavior modeling, interaction exploration, MLP aggregation, and introduces a novel search space containing three tailored subspaces that cover most of the existing methods and thus allow for searching better models. To find the ideal architecture efficiently and effectively, AMEIR realizes the one-shot random search in recommendation progressively on the three stages and assembles the search results as the final outcome. Further analysis reveals that AMEIR's search space could cover most of the representative recommendation models, which demonstrates the universality of our design. The extensive experiments over various scenarios reveal that AMEIR outperforms competitive baselines of elaborate manual design and leading algorithmic complex NAS methods with lower model complexity and comparable time cost, indicating efficacy, efficiency and robustness of the proposed method.