Lots of very girlish ideas here. Now for the truth:
A. Never "call" for a ball unless you are certain you can catch it. Keep going after it until you know you're going to catch it. Then, call for it by yelling, "mine!" or "my ball!" loudly and clearly. Waving your arms once or twice is a good idea if it's especially high and you have time.
B. Outfielders and infielders should be instructed that when no one is on base, it doesn't matter who catches the ball as long as it is caught. If the outfielder can get there, but clearly sees that the infielder is camped under it and hears her calling it, then the outfielder should just back off and let the infielder catch it. However, when there are runners on base and there is a threat that one of them could tag and move up on the play, then it is essential that if the outfielder can easily catch the ball with momentum going toward the runners (as opposed to the infielder going backward) she should take charge by "calling off" the infielder--even if that infielder has already called for it. "MINE, MINE, MINE!" The outfielder should yell. Upon hearing this, the well-coached infielder will veer out of the way or just fall to the ground to avoid a collision. The well-coached infielder knows that the outfielder has a much better chance of throwing out the runner tagging at third because the outfielder is going to catch the ball with forward momentum.
The bottom line is that the ball must be caught-- and caught without confusion or collision. That means the infielders and outfielders must be on the same page with regard to protocol.