Shades of Green is fabulous - it doesn't feel like a military hotel, and actually used to be the Golf Club Resort (a deluxe resort), owned by Disney. The military now leases it back. We used to stay there many times - so if you're eligible (you can call and provide them with all the details to find that out) - I highly recommend it. In many ways, you are treated like you are staying on property. Transportation is easy, the gift shop is cheaper, and the grounds and pools are beautiful. They sell a version of the military tickets right in their lobby, which you are welcome to just stop in and buy if you're eligible, even if you stay elsewhere. They are comparable to the ones you can get from the base / post, but even better, because you can buy them for the exact amount of days at the park you need. They also sell the Universal Studios military discount tickets there. As my husband advanced in rank, it wasn't so important to stay there any longer (it got to be more expensive, as the rate is based on rank), but we have always enjoyed it there. The rooms are among the largest you will find, and it's easy walking distance to the Grand Floridian (and Polynesian, too, if I remember correctly) to hop on the monorail. It has been a few years, so I don't remember about how other benefits worked - like ADRs - and now Fastpass+ (eek!) but I'm sure the Shades website has information in a FAQ section.
All that said - I usually just call Disney reservations with the dates of my trip and ask what type of military discounts they are offering at that time. Have a couple of different properties in mind (deluxe, moderate - doesn't matter). I've never stayed club level before, but for our upcoming trip in May, the "military discount" deal for a Club Level Lagoon view at the Polynesian made it affordable enough to give it a try. As a previous poster said, it's typically around 40% off. I just recently called reservations to make sure that was still the best deal for the dates, and it was still $700 less than their spring special for the week. And there are only a certain number of rooms for the military discount, so it is imperative to check as soon as possible. We booked our May deal in October.
Good luck with your search - there's a wealth of information out there!