With the advent of mobile crowdsensing, we now have the possibility of tapping into the sensing capabilities of smartphones carried by citizens every day for the collection of information and intelligence about cities and events. Finding the best group of crowdsensing participants that can satisfy a sensing task in terms of data types required, while satisfying the quality, time, and budget constraints is a complex problem. Indeed, the time-constrained and location-based nature of crowdsensing tasks, combined with participants' mobility, render the task of participants' selection, a difficult task. In this paper, we propose a comprehensive and practical mobile crowdsensing recruitment model that offers reliability and quality-based approach for selecting the most reliable group of participants able to provide the best quality possible for the required sensory data. In our model, we adopt a group-based approach for the selection, in which a group of participants (gathered into sites) collaborate to achieve the sensing task using the combined capabilities of their smartphones. Our model was implemented using MATLAB and configured using realistic inputs such as benchmarked sensors' quality scores, most widely used phone brands in different countries, and sensory data types associated with various events. Extensive testing was conducted to study the impact of various parameters on participants' selection and gain an understanding of the compromises involved when deploying such process in practical MCS environments. The results obtained are very promising and provide important insights into the different aspects impacting the quality and reliability of the process of mobile crowdsensing participants' selection.