2 cups wont hurt and neither will the 1:1. However, there is no required amount since the only reason for the water is to get the sugar into solution and to sanitize it. That means all you need is enough to do these two things. I always measure my sugar and put it into a sanitized container (usually a pyrex measuring cup) and then get the water to a good rolling boil and add just enough to the sugar to fully dissolve--adding any more does nothing since what you are looking for is a simple syrup and this is achieved as soon as the sugar dissolves. Once I'm ready to add the solution to the bottling bucket, I don't bother cooling it but simply rack some beer into the bucket and pour the solution in while the rest of the beer is racking. Give a good (though not vigorous) stir with a sanitized spoon and then bottle.
"Cast your bread upon the waters for after many days you will find it again. Give portions to seven, yes to eight, for you do not know what disaster may come upon the land." Ecclesiastes 11:1f
Who knew there was an ancient recipe for beer in the Bible?
My paraphrase: "Since you don't know what disasters might befall you , when you make beer share it with friends. Someday you might need them to share with you."