As quantum computing services continue to proliferate, users are increasingly faced with design decisions regarding their use. In particular, one must decide which service(s) to employ and how many shots to allocate to execute a given task, potentially combining shots from multiple services. Exploring this design space requires evaluating the trade-off between output reliability and execution cost. This paper presents a heuristic algorithm for efficiently exploring this design space under budget constraints. We also report empirical results using real quantum services to illustrate the effectiveness and practicality of the proposed approach.