. If I got geese would they be good protectors for my flock of ducks?
They probably will not fight of predators but they will sound the alarm if something is wrong. You will have to be within hearing distance when their is a predator otherwise they are useless for protection. They will definitely scream when they see danger but they will also scream at almost everything else (a squirrel walking by, leaves blowing of trees, or when they just feel like announcing to their whole neighborhood that they are in a good mood).
. Would they bond well with my ducks?
If you use a broody duck to raise them they will probably form a closer bond than if you introduce them into the flock when they are older. One goose will definitely bond with a flock of ducks but a pair of geese will have a stronger connection to each other than with the ducks. That said, the geese will be much happier if they have another goose rather than being the only goose.
. What kind of breed would be best?
Some breeds like africans and chinese are much louder than others so better for sounding the alarm. I have 2 toulouse geese of which are very gently and sweet and can be loud when they want. Romans are smaller and supposed to be quieter and well tempered. Pilgrims can be auto sexed meaning the male is white and female is gray.
Check these links for breed info
http://www.metzerfarms.com/GooseWelcome.cfm
http://www.metzerfarms.com/GooseBreedComparison.cfm?CustID=556662
. And what genders should I get if I get two geese? Two boys, two girls, or a pair? (I don't want to hatch eggs)
Since you don't want to hatch then i suggest you get two females. A gander (male) will mate with the goose and likely the ducks too which will only be a disturbance in the flock as you don't want to hatch out more geese.
-New Question- . Where would I get a pair of sexed geese?
Metzer farm seems popular and i think will ship a minimum of 2 geese. I bought mine from Ideal poultry and have always had good experience with them.