I don't think they have an annexes or annex anymore, they did when i was stationed their in the 80's. Back then they had two rolls of hangers, now the have 5 rolls of hangers now so they really don't have to have the annexes anymore. In my opinion best to goto the back set of hangers first and work backwards in history, there is just too much to see in the first couple hangers that are WWI and WWII that sort of stuff, depending on what a person is interested then that is where they should start their tour.
There are quite a few great military museums.
The Naval Aviation one in Pensacola FL is good.
The Space and Rocket Center in Huntsville AL.
National Infantry museum at Ft Benning (soon to be joined by the Armor and Cavalry museum in a few years 2020-2025) in the meantime nearby Patton Park is cool.
The National Museum of the U.S. Army @ Ft Belvoir should be open in two years.
The Field Artillery museum at Ft Sill is nice (they have expanded since I was there 20 some years ago).
The Airborne museum at Ft Bragg is also nice