In terms of Norwich compared to the citadel or VMI, I may be able to help out. I have experience with all three. VMI is smaller and 100% Cadets. Best way to describe VMI is an old-fashioned version of West Point (which may be why VMI is called the West Point of the South!)
Norwich and Citadel, in my opinion. are most similar in terms of size and mix of cadet students, non-Cadet students, and online students. Both schools have unique traditions and offer their students, cadets and non-Cadets the opportunity to purchase rings and participate in athletic programs, etc. Biggest difference between Citadel and Norwich is one is in the south and one is in the north!
All three are great options. So best of luck wherever you decide to go!