We raise dairy goats, so they are not terribly meaty. We don't have a set age to butcher them, it's whenever we want to eat one, basically, or we have too many to feed. We are getting ready to process a vicious stinky buck with horns, he started attacking me when I try to feed him or clean his pen, so he is going in the freezer. Normally we eat wethers, any male we are not selling as a breeding buck will be wethered and grown for eating. We may eat a doe if she is not really a good producer or quality enough to breed.
As for taste, to me goat tastes more like beef than like lamb. If you have eaten elk or venison, it's pretty similar. I find from the dairy goats, it is best ground, made into stew meat, or slow cooked at a low temperature with lots of liquid (I make broth from the leg bones to cook the meat in), since they don't have a lot of fat on them. A smallish animal, say 4-6 months old, is also pretty nice stuffed with herbs and roasted over a fire outside whole for a special occasion.