Recently smart homes equipped with many sensors and IoT devices are widespread. However, when smart home users receive smart home services like elderly monitoring, they need to upload their privacy sensitive data to potentially untrusted cloud servers where the service quality (user's benefit) depends on the amount/frequency of the uploaded data. In this paper, aiming to minimize the risk of privacy leakage and maximize users' benefit obtained through services, we propose a novel privacy-aware data management method that works on a smart-home system composed of smart homes with sensors, edge computing servers, and a cloud server. We formulate a combinatorial optimization problem which determines the best choice of data type (raw or activity label recognized at the edge) and upload frequency in each time slot taking into account the constraints of edge server resources and users' budgets as well as the k-anonymity of activities and users' preferences. Since the target problem is NP-hard, we propose a heuristic algorithm to derive semi-optimal solutions by determining choices with better objective function values in a greedy manner. Through experiments using smart-home open dataset, we confirmed that the proposed method outperforms the conventional methods using only a cloud server.