Query logs contain rich feedback information from a large number of users interacting with search engines. Various click models have been developed to decode users' search behavior and to extract useful knowledge from query logs. Although the state-of-the-art neural click models have been shown to be very effective in click modeling, the input representations of queries and documents rely on either manually crafted features or on automatic methods suffering from the high-dimensionality issue. Moreover, these neural click models are still rather restrictive when coping with commonly biased user clicks. In this paper, we investigate how to effectively deploy a neural network model for decoding users' click behavior. First, we present two novel rank-biased neural network models ($RBNN$ and $RBNN^* $) for click modeling. The key idea is to deploy different weight matrices across different rank positions. Second, we introduce a new method ($QD\mymathhyphen DCCA$) for automatically learning the vector representations for both queries and documents within the same low-dimensional space, which provides high-quality inputs for $RBNN$ and $RBNN^* $. Finally, a series of experiments are conducted on two different real query logs to validate the effectiveness and efficiency of the proposed neural click models. The experiments demonstrate that: (1) The proposed models can achieve substantially improved performance over the state-of-the-art baseline on two datasets across multiple metrics. By incorporating rank-specific weight matrices, $RBNN$ and $RBNN^* $ are more capable of dealing with the position-bias problem. (2) The input representations of queries, documents and context information significantly affect the performance of neural click models. Thanks to the application of $QD\mymathhyphen DCCA$, not only $RBNN$ and $RBNN^* $ but also the baseline method exhibit enhanced performance. Furthermore, the training cost under the proposed models is greatly reduced.