Materials discovery and design typically proceeds through iterative evaluation (both experimental and computational) to obtain data, generally targeting improvement of one or more properties under one or more constraints (e.g. time or budget). However, there can be great variation in the quality and cost of different data, and when they are mixed together in what we here call multifidelity data, the optimal approaches to their utilization are not established. It is therefore important to develop strategies to acquire and use multifidelity data to realize the most efficient iterative materials exploration. In this work, we assess the impact of using multifidelity data through mock demonstration of designing solar cell materials, using the electronic bandgap as the target property. We propose a new approach of using multifidelity data through leveraging machine learning models of both low- and high-fidelity data, where using predicted low-fidelity data as an input feature in the high-fidelity model can improve the impact of a multifidelity data approach. We show how tradeoffs of low- versus high-fidelity measurement cost and acquisition can impact the materials discovery process. We find that the use of multifidelity data has maximal impact on the materials discovery campaign when approximately five low-fidelity measurements per high-fidelity measurement are performed, and when the cost of low-fidelity measurements is approximately 5% or less than that of high-fidelity measurements. This work provides practical guidance and useful qualitative measures for improving materials discovery campaigns that involve multifidelity data.