As with athletics, I think you'll also find some overlap in academic distinction between DII and DIII colleges. But as others have advised, a "great education" means different things to different people. What does "great education" mean to you? High paying job after undergrad? Impressive diploma? Great resume for graduate school? Intellectual challenge?
Think carefully about your goals, and that may allow you to widen your net beyond DIII.
One thing that might be useful for you to research is college soccer. There are probably hundreds of international students playing college soccer, at all levels. There may be more information available about soccer than baseball. The NCAA also publishes some guides for international athletes on their website.