Brain-computer interfaces (BCIs) can provide an alternative means of communication for individuals with severe neuromuscular limitations. The P300-based BCI speller relies on eliciting and detecting transient event-related potentials (ERPs) in electroencephalography (EEG) data, in response to a user attending to rarely occurring target stimuli amongst a series of non-target stimuli. However, in most P300 speller implementations, the stimuli to be presented are randomly selected from a limited set of options and stimulus selection and presentation are not optimized based on previous user data. In this work, we propose a data-driven method for stimulus selection based on the expected discrimination gain metric. The data-driven approach selects stimuli based on previously observed stimulus responses, with the aim of choosing a set of stimuli that will provide the most information about the user's intended target character. Our approach incorporates knowledge of physiological and system constraints imposed due to real-time BCI implementation. Simulations were performed to compare our stimulus selection approach to the row-column paradigm, the conventional stimulus selection method for P300 spellers. Results from the simulations demonstrated that our adaptive stimulus selection approach has the potential to significantly improve performance from the conventional method: up to 34% improvement in accuracy and 43% reduction in the mean number of stimulus presentations required to spell a character in a 72-character grid. In addition, our greedy approach to stimulus selection provides the flexibility to accommodate design constraints.