It seems that we are going to have either 25 or 50 MySQL databases. However, each DB is limited to 100 MB of data, so we'll have to plan ahead somewhat. The 25 DB limit may turn out to be the only real bottleneck obstacle in choosing the intermediate level hosting package.
There are approximately 2000 players in the NFL we will have to keep track of. For each player, we'd need to be able to track every statistical category- passing stats, rushing stats, receiving stats, return stats, kicking stats, and defensive stats. For each player and each statistical category, we need to keep track of stats for 17 weeks. We need to come up with at least a rudimentary DB schema and run some benchmark tests to figure out how big a season's worth of data will get, and also what kind of space an average league will require.