I cook a lot of goat on my bullet.
I buy it at a halal butcher, and they'll only sell you a half or whole goat. It's usually frozen, but they occasionally have fresh. A whole goat carcass runs around 20-25 pounds there. I have them cut the half-goat into thirds-- the leg, the ribs, and the foreribs/shank. for a whole, I have them split it bilaterally first.
I then flavor brine for two or three days. I use a cup of kosher salt and half a cup of sugar per gallon of water, and a ton of tumeric. The halal place has a good deal on sacks of tumeric. I like the yellow color it gives the meat and the mild peppery flavor.
The stuff comes from the butcher pretty much untrimmed. I've experimented with trimming the ribs, trying to pull off a membrane as one would do for pork ribs, and it doesn't seem to matter. That membrane is hard as hell to remove on goat, and the meat wasn't any better.
After the brine, I just coat them with garlic olive oil. I've used tabasco and black pepper, and that worked fine, but I like the garlic a bit more.
Set the smoker for 240. Cook the leg for 12-18 hours. I have yet to overcook one. It takes about 12 hours before it starts to pull like pork. Cook the ribs for 6-8 hours, the forerib and shank section for 8-10. no finishing sauce, no mops. I've done alder, maple, and hickory, and combinations. I prefer straight up hickory.
The leg is hard to screw up. If it's not cooked long enough, it doesn't pull, but it's like a firm pork butt-- not bad at all. the shank tends to turn out really well. I have screwed up the ribs before. It was by far the largest goat carcass i've ever got from them, so maybe it was just a tougher goat, but I also cut the cook time a little short. The ribs were cooked, but tough.
Since these guys are the only place I know who sell goat, and they have a great price on whole carcass lamb, my next project is going to be learning how to trim up these carcasses a bit better.
Anyhow, check your phone book for a halal butcher, they're likely to have goats. If you're lucky, they'll sell the leg separately, and you can just start with the best part.
If you like the slight gamey flavor of lamb, you'll like goat. That flavor is more pronounced, even moreso than in mutton. And it's a tougher meat, but that also means that you can get it to pull, unlike lamb.
Last super bowl, I smoked two goat legs until they pulled and used that as a basis for chili. That was pretty good.
This year, I'm just going to try smoking a whole lamb carcass, no chili.