Geese are not good guardians for chickens. First, geese are as susceptible to predation as any other bird and therefore cannot actually stop any predators. Secondly, geese (especially ganders) can be very aggressive towards smaller poultry and you may find yourself protecting your chickens from the geese rather than outside predators. Third, geese tend to muck up their water and make a sodden mess of their pens which is not an ideal situation for chickens who don't particularly care for getting wet.
I could go on...
I got geese for the same reasons you are looking into getting them. It was a disaster. I intended to house my waterfowl and chickens in separate houses, but allow them to share the same run space (over 1000 sg. ft.). That never came to pass because of aggression issues that I encountered. Geese are great fun, but they are tough birds to have. I had to cull out my ganders because they were so nasty. I still have a goose in with my ducks, but they are kept completely away from the chickens because the goose kept going after the chickens. She tolerates the ducks, but only after a prolonged introduction period. (She tried to kill them when I first put them in together.)
I would not make any grand plans involving geese and ducks and chickens all living together in harmony because it may not come to pass. Try it on a small scale and see how it works, but I would also have a Plan B ready to implement should the need arise. I had to separate birds rapidly when the aggression began to stop my smaller birds from getting beaten to death. Although I fortunately have lots of space, I ran into a housing shortage. I did not anticipate having to build another secure house because the geese were bent on destroying any smaller bird that crossed their path.
Geese are great. They add a wonderful dynamic to any setting, but they can be challenging. I am not trying to discourage you from getting them. I am just trying to warn you of the potential downsides of having them in with smaller flock mates.
Good luck.
