Yep you got it! Badaling's about the worst part to see the great wall!
It's the closest to Beijing, people get dropped there by buses of 60 every half a minute. It's been fully renovated / reconstructed, and you can't usually spend much time walking around.
Never been to Mutianyu but heard it's better.
Don't know what the state is for Simatai - Jinshanling now, the trek was closed last time I brought people there, but there's a great walk to do on the wall between those 2 places.
You also can find some guided tours in Beijing bringing you in small groups to more remote parts.
Yeah it was pretty fucked up last time I got there...