My goats love the oak trees, greenbriar, and all the other brush, but they also love sunflowers.
I've got just about the same thing as you growing for my goats. Last fall in one of my paddocks I sowed a mix of oats, triticale and wheat. The goats loved it, and promptly grazed it to the ground. I almost did not get them moved before they killed it. Then we hit that dry spell, so it was really slow to grow back. It is about ready to graze one more time before the trees and ect come back for spring. In another paddock I did ryegrass/clover (though the clover did not come up) They did eat it to the ground.
In another paddock last spring I seeded a sandyland mix of mostly native grass. Lovegrass, little bluestem, Haskell side oats, side oats gramma, indian grass, etc. That was when we were really wet, and I did not move the goats into it in time. They grazed it, but did not seem to like it as much as I hoped... though I do not know if I let it grow up too much, or it is just the plants.
Here are the goats in the native grass paddock, wading through grass.
I've wanted to try millet, but have never gotten around to it.