Steve, if you do it right, the meat is not greasy. It's well worth reading up on goose cookery before tackling your first.
To ensure that the rendered fat flows quickly and efficiently off the bird, I pierce the skin all over with a needle-sharp skewer, inserting it at an angle to avoid hitting the meat. I keep the oven temperature low -- about 325 Fahrenheit -- so the fat does not scorch in the pan, and spoon off as much fat as possible after one hour and two hours of roasting. Some cooks recommend steaming the bird in the Chinese fashion, but that's messy and, in my opinion, unnecessary. When the breast meat is at or above 170 Fahrenheit, spoon off the last of the fat and crank the oven up to 400F for about 10 minutes to crisp the skin. It should then rest for at least fifteen minutes before carving.
A 12-pound goose will take about two and a half to three hours, depending on how chilly it is when it goes in the oven.
Much tosh is talked and written about stuffing for goose, but I don't recommend it; by the time the bird is ready, a stuffing is drenched in fat. Dressing to go with goose should be baked on the side, in my admittedly arrogant opinion.
With the first load of rendered goose fat taken out of the pan, you're ready to prepare the potatoes. Quarter and parboil them, then toss them in a bowl with a tablespoon or two of goose fat, some salt and pepper, and maybe some herbes de Provence (if you're me). Pop them in the oven in a skillet or baking dish when you have raised the oven temperature to crisp the skin of the goose.