Goodness, you've been getting some very unhelpful advice. To give you an idea of the appeal process from a panelist's perspective (disclaimer: I stopped sitting on appeals so I don't claim to be a current panelist), we would be sent a pack prior to the hearing, containing all information that has been submitted from either party and copies of the application form. Other documents such as maps of preferred and offered school, statistics of PAN, last place offered, etc.
If you send letters of support, ofsted reports, prospectuses, etc., you will have three panelists and a clerk who are duty bound to wade through it all, even though it's 99.999% likely to be irrelevant. At the end of that, they're going to be increasingly irritated.
The school admissions appeals code is very clear about grounds for appeal. Either a mistake that has deprived your child of a place, or that your child would be disadvantaged by missing out on a place at the preferred school to such an extent that it would do him more harm than would be done to the children at the school from having to accommodate an extra child.
Things that won't help:
-slating the offered school
-suggesting that your child is 'too good' for the offered school
-letters from other parents (saying what? "Jimmy is such a good friend....")
-prospectuses
-general exam result trends.
Bear in mind that most parents would prefer their child to go to a good school rather than a less good school, but there isn't space for everyone. Also, if a school is open and operating, then ofsted have deemed it to be a legitimate educational establishment. Panels can't be seen to undermine teaching quality of a school by agreeing that a school isn't good enough for a child (even if they privately think that's the case).
Things that will help:
-particular clubs, groups or activities that would benefit the child which the other school doesn't have (e.g. DS is particularly keen on creative writing and school x has a two hour creative writing club each week).
-particular needs that could be met by the appeal school (e.g. the child who moves a lot with the Forces appealing to attend a school which has a lot of experience in catering for Forces children.)
-rarely, evidence of extreme bullying and that the perpetrators go to the offered school.
-medical evidence that a child needs to be at their closest school in case of urgent medical care.
-Rarely, that a child would be endangered at their offered school because of their parent's professional contact with other parents/children at that school (e.g. police/social worker)
There really is very little grounds in appealing because you don't like the offered school or you really wanted the other school. If your child is just an average child who didn't get their choice of school, and the appeal school is full, you shouldn't win.
However, it is a big balancing act. While your case may not be strong, anything you can do to undermine the schools case that they are full will help you. So, look at their class arrangements. If the school had some big year groups and the PAN is a lot smaller, you may find that they could fit other children in. Make sure the school layout on the Net Capacity sheet is correct - make sure they haven't missed an extension off.