Been there, done that, got the T-shirt. Managed to beat the local authority on an infant class size case (because they'd got the regulations wrong and were trying to claim infant class size were it didn't apply). Mind you, I had to go to the Local Government Ombudsman twice to get the correct result.
From my own experience and advice that was given to me:
The authority will argue that the school will be prejudiced by admitting your son. You have to show that the prejudice to your son by being educated elsewhere is greater than the prejudice to the school.
Concentrate on any needs your son has which will not be met by the allocated school. Assuming the Authority hasn't made a mistake, that's your best chance of success. Think widely when considering needs. For example, if the allocated school is a long way away you can argue that he will find it harder to integrate into the school and his local community, damaging his social development (I can expand on that privately if it helps).
If the Authority argues that it is an Infant Class Size appeal there are only limited grounds on which you can succeed. Your best chance is showing that admitting your child won't cause Infant Class Size prejudice (unlikely but that's how I won). If you can't, you will have to show that the Authority has made a mistake, broken the mandatory provisions of the Admissions Code or behaved unreasonably.
Do NOT say anything about league table rankings or similar. Do NOT say or imply that your son will get a better education at your chosen school. It may be true but it isn't a reason for allowing an appeal and may turn the panel against you.
Do NOT take a photo of your son to the appeal. The panel will feel like you are trying to blackmail them.
Make sure you understand the Authority's case fully. They have to send you a copy of their written submission before the appeal (if they haven't done so already). Look for any weaknesses in their case and make sure you've got a list of questions to ask.
If the Authority makes significant points which are not covered in their written submission, complain. They aren't supposed to do that as it stops you from preparing properly. Similarly, make sure you submit all your evidence properly in advance. Don't try to ambush the Authority at the hearing with documents they haven't seen.
Make sure you understand the School Admissions Code and School Admission Appeals Code (both available for free download from the DCSF website). You would be surprised how often Authorities get things wrong. If they have got something wrong, you may be able to use this in the appeal. If you lose the appeal, it may give you grounds for going to the Local Government Ombudsman.
Good luck and feel free to contact me direct if you have any questions.