Welcome to BYC! I agree with sourland and others about space. If there is lots of it, you should be fine with turkeys, geese and chickens together. I also agree that three roosters are probably too many. Their behavior will change once hens are thrown into the mix, and they will probably start to fight over them. You'd need at least 30 hens to make them all happy, depending on breed. If you kept all three separate, you could get by with less hens per rooster. I hope you will take the time to explore the forums. They are a great resource.
So happy you decided to join this wonderful community. 
I keep chickens, turkeys, and ducks together in the same coop - overall, there aren't too many squabbles. Finding though, that as both turkey hens mature, they become progressively moodier. They do pick on most of our chooks during feeding and roosting time, in order to maintain dominance. Thankfully, our birds all have endless ground on which to free range, therefore said chickens are able to escape the wrath of the gobblers. 
and Welcome to Backyard Chickens. 
