There's a lot of good info on geese here. I did lots of searching and reading old posts last year when I was researching geese.
My pair of American Buffs are large, but I don't take any chances with stray dogs coming around, so they are fenced in all the time. They have fenced in area approximately 20 x 40 feet. They also have a 5 x 15 dog kennel attached to a very large dog house for night time protection. They keep the grass in the large area trimmed down. I would like to give them more room, but don't have the back 1/3 acre fenced in yet.
The rule of thumb I've read is that an acre of good grass/pasture can sustain 8-10 geese, depending on how large they are.
They don't have to have a pond nor do they need one. I use a large utility tub from the local big box home improvement store and they use that to bathe and splash around. But in the winter, they were happy to take buckets baths when it was too cold to have their tub filled up.
Geese are great birds. They have distinct personalities and are a joy to have around. I haven't regretted a day that I got them a year ago as goslings. They were fun to watch grow each day and now they're big gown up geese. Now, my goose is sitting on a nest full of eggs. We'll see in about 3 weeks if I'll have more geese. If so, I'll need to find a bigger piece of property to move to.