In recent years, the Gulf of Mexico Loop Current System has received increased attention. Its dynamics and the warm water it transports from the Caribbean influence the local weather and ecosystems. The high velocities of the Loop Current and the eddies it sheds can disrupt important industries. Accurate forecasting of the Loop Current system is challenging, in part because of the lack of data over long enough periods of time, which leads to considerable uncertainty. In this work, we describe and apply our MIT Multidisciplinary Simulation, Estimation, and Assimilation Systems (MSEAS) and Error Subspace Statistical Estimation (ESSE) ensemble forecasting methodology and software to estimate such uncertainty and to inform data collection in a quantitative manner. The ensemble forecasts allow for mitigating risks and optimizing data collection. We demonstrate that our probabilistic system has qualitative skill for over a month. We show that uncertainty grows along and around the Loop Current and its eddies, and transfers to depth from the shelf and slope. Using information theory, we find that our probabilistic hindcasts can have predictive capabilities for one to three months, with a slower loss of predictability in the quieter Loop Current states. Through the use of correlation and mutual information fields, we optimize future sampling by predicting the impacts and information content of observations. We find that the most informative data are those that either directly sample dynamically relevant areas or sample coastal modes that are correlated with these areas. Subsurface data are shown to have more impact on forecasts of one month or longer.