Like lamb you can marinate it in garlic, olive oil, oregano, rosemary, lemon juice and salt and pepper, alot depends on the cut of goat, it is usually cut in the same style as lamb, for what you ate it was likely a shoulder or leg, you cook it slowly in the oven, until it falls apart and can shred it, you can roast the potato's with the goat in the same roast pan, even the peppers, I like the red sheppard ones available now, they can be added half way into the cooking time, seasoned the same way.
The meat will take about 3-4 hours to cook, start it at 400 d F to brown it then drop it to 325 d f for the remaining time, it depends on the size of the piece of meat your cooking, a nice bone-in shoulder or leg is best, here in Toronto Canada I can get it at Greek butchers, and the large West Indian community here cooks alot of it, I worked in Jamaica and cooked it many ways from roast to curry dishes.