We consider the problem of jointly predicting the quality and timing of responses to questions asked in online discussion forums. While prior work has focused on identifying users most likely to answer and/or to provide the highest quality answers to a question, the promptness of the response is also a key factor of user satisfaction. To address this, we propose point process and neural network-based algorithms for three prediction tasks regarding a user's response to a question: whether the user will answer, the net votes that will be received on the answer, and the time that will elapse before the answer. These algorithms learn over a set of 20 features we define for each pair of user and question that quantify both topical and structural aspects of the forums, including discussion post similarities and social centrality measures. Through evaluation on a Stack Overflow dataset consisting of 20,000 question threads, we find that our method outperforms baselines on each prediction task by more than 20%. We also find that the importance of the features varies depending on the task and the amount of historical data available for inference. At the end, we design a question recommendation system that incorporates these predictions to jointly optimize response quality and timing in forums subject to user constraints.