Most but not all domestic geese are very fatty. I have not done one in a WSM but have done them in a kettle. You can high-heat grill/roast or, if fatty, you can low/slow. You won't get good skin on the latter approach.
If the goose is fatty you can prep it as for Peking duck by removing the excess fat, pricking the skin all over (but not the flesh) and dipping it in boiling water (neck down for one min, then tail down for one min), or pouring boiling over it two or three times, or steaming it by setting it on a rack in a roaster, covered, with simmering water underneath. In any of these cases you'll get the best skin on a high-heat cook if you air-dry the goose in the fridge.
If the goose is fatty it will throw off a lot of fat while cooking. You really need something under the bird to catch it or you'll have a mess.
A baste is nice for a high-heat goose; a sauce is good for a low/slow after cooking (and after removing the skin and the meat from the bones). Like duck, goose does well with fruits (common are the stone fruits like cherries, prunes, plums but pomegranate is delicious with goose as well), sherry, honey, onion, celery root, sage, thyme, and also star anise, cardamom--a few of the more exotic spices.
