I have four goats and the least picky, best forager is the Boer goat. My mini Nubian is the next least picky, but my two spanish/myatonic mixes are pathetic babies: I had to cut them paths into the woods before they would go in to eat. Even then, I find those two eating dried leaves rather than browsing the lush, green vegetation that is readily available to them...goofy goats.
I will say that I gave the four of them an area that is 100x300 and was overgrown up to nearly 5' tall in spots and in less than 6 months grass was growing in areas that hadn't seen sun in a very long time. Now, three years later, it is cleared of everything other than the large mature trees and I have to herd them to other pastures to eat....since nothing has a chance to grow with them there.
Please keep that in mind before committing to getting goats: After they have cleared the 30x40 area, you will need to feed them something. Also, if they manage to get loose, please be prepared to lose the plants you like the best in your yard. Every time mine have ever gotten loose I lose a fruit tree or two. It's as if they are drawn to them and will pass by every other plant on our 7 acres and head straight for my youngest, and obviously tastiest fruit trees.
I want to be mad at them, and manage to be really upset for a while, but at the end of the day, they are just goats doing what goats do best.