In this paper, we are interested in scheduling and checkpointing stochastic jobs on a reservation-based platform, whose cost depends both (i) on the reservation made, and (ii) on the actual execution time of the job. Stochastic jobs are jobs whose execution time cannot be determined easily. They arise from the heterogeneous, dynamic and data-intensive requirements of new emerging fields such as neuroscience. In this study, we assume that jobs can be interrupted at any time to take a checkpoint, and that job execution times follow a known probability distribution. Based on past experience, the user has to determine a sequence of fixed-length reservation requests, and to decide whether the state of the execution should be checkpointed at the end of each request. The objective is to minimize the expected cost of a successful execution of the jobs. We provide an optimal strategy for discrete probability distributions of job execution times, and we design fully polynomial-time approximation strategies for continuous distributions with bounded support. These strategies are then experimentally evaluated and compared to standard approaches such as periodic-length reservations and simple checkpointing strategies (either checkpoint all reservations, or none). The impact of an imprecise knowledge of checkpoint and restart costs is also assessed experimentally.