Well, I can comment on part of this, from a parents view point, before the experts come along!!
If the specialism of the school you want is really important to you, academic evidence showing how much that aspect means to your child is a must and also other proof from outside school that the specialism is taken seriously - for instance science, that they do well in science at school, belong to science clubs, visit science museums etc.
But remember you have already satisfied the academic entry into a Bucks grammar school so they are not looking for a subject by subject break down.
Likewise, if the journey to the school you have been allocated is truly awful and the school you want means a safer, easier ride, find out about the various options and be knowledgeable about what is on offer because the panel could well know the options!
Edit: Our DS's journey to the allocated school would have impacted big time on our family (getting DD to school, our work, picking him up from after school activities) and would he get the full benefit of a grammar school if there were these problems (quite a common appeal point, I believe, but important).
Our quip was never negative about the school offered just that the school we wanted was really what our son dreamt about.
Our panel were keen to establish that the friends our son wanted to be with, which we mentioned in our presentation, where in fact friends he had made over the years from his junior school.
Siblings to follow. We were hoping (and she has done it
) that if our DD passed her 11+ that she would go to the school in question and they would be together.
Good luck, I am sure others who have been successful will give you pointers along with the forum experts, who really are just that, experts!!