Hi Victoria, congrats on your land. Before you burn the pasture, you may want to give the goats the run of it—they'll eat up whatever they're interested in, and you'll get some food value out of what's already there.
Are you planning on doing rotational grazing with them? I'd recommend reading up on management intensive rotational grazing (Voisin method) if it's not something you're already planning on doing. Goats are very picky eaters, and if you give them free run of a large pasture, they'll decimate it. They'll walk around the entire area eating whatever is most palatable to them first, and they'll eat all of it. Then they'll start going for their second choice, and so on. In the meantime, their first choice will begin regrowing its foliage, and they'll eat that regrowth as soon as it appears. Within a few months, they'll have worn out the energy reserves of the plants they prefer, while whatever they aren't fond of will proliferate. In a very short amount of time, you'll end up with a pasture full of things they don't care for, regardless of what you planted to begin with. It seems like you already know that grass isn't their preferred diet, which is what makes managing them different than cows or even sheep. Grass, and to a lesser extent legumes, are adapted for grazing. Goats prefer plants that are generally not adapted for grazing (forbs and browse), so the more recovery time you can give an area between grazings the better.
We're currently setting up a few areas of goat pasture, and here's what we're planning on doing. The pastures will be planted with the goat pasture mix from NaturesSeed. It's 40% grass, 45% legume, and 15% chicory. We are also adding dandelion, narrow leaf plantain, and Queen Anne's Lace (our goats LOVE the QAL the grows rampant on our property, so we harvested the seed to mix in). The pasture will have permanent perimeter fencing, and will be subdivided with 6' wide alleys run long ways, also with permanent fencing. Instead of using the alleys as a walkway though, we are planting them with trees and other browse and forbs that the goats enjoy. The goats will be in the long strips of pasture, and they'll get a new paddock each day sectioned off with polywire. So in addition to what they get from the pasture mix, they'll also have two edges of their paddock where they can access browse. But since it's fenced off, they won't be able to kill the plants—they'll just eat as far back as they can reach through the fencing, and those plants won't be completely defoliated.
If you set up silvopasture and give the goats free run of it though, they'll kill off whatever nice things you plant for them much quicker than you'd think.
Hope this helps!