In this paper we identify basic design issues of Mobile Crowdsensing Systems (MCS) and investigate some characteristic challenges. We define the basic components of an MCS - the Task, the Server and the Crowd - and investigate the functions describing/governing their interactions. We identify three qualitatively different types of Tasks; a) those whose added utility is proportional to the size of the Task, b) those whose added utility is proportional to the progress of the Task and c) those whose added utility is reversely proportional to the progress of the Task. For a given type of Task, and a finite Budget, the Server makes offers to the agents of the Crowd based on some Incentive Policy. On the other hand, each agent that receives an offer decides whether it will undertake the Task or not, based on the inferred cost (computed via a Cost function) and some Join Policy. In their policies, the Crowd and the Server take into account several aspects, such as the number and quality of participating agents, the progress of execution of the Task and possible network effects, present in real-life systems. We evaluate the impact and the performance of selected characteristic policies, for both the Crowd and the Server, in terms of Task execution and Budget efficiency of the Crowd. Experimental findings demonstrate key performance features of the various policies and indicate that some policies are more effective in enabling the Server to efficiently manage its Budget while providing satisfactory incentives to the Crowd and effectively executing the system Tasks. Interestingly, incentive policies that take into account the current crowd participation achieve a better trade-off between Task completion and budget expense.