First preferences don't get allocated before other preferences, but if you really want a school, you should put it first because otherwise you may get into the school you put first, and not the school you really want.
I think the way the school have phrased it is a bit confusing, but if you weren't offered any choices, it doesn't really matter which school was put first.
A school won't offer you a place and then the LA say no. Some schools/MATs are their own admissions authority, whilst the LA is the admissions authority for LA schools and may administer admissions for some academies. None of this is really relevant unless you think a mistake has been made?
In terms of your appeal, think about interests/hobbies/aptitudes your child has, and why they'd be more supported at the school(s) you want. For example, your child plays rugby, and school 1 has a rugby team and allocated school doesn't. Your child has an aptitude and interest in languages (you'd need to provide evidence for this) and school 1 offers two language options at KS3, whilst your allocated school only offers one. Your child is especially good at DT (again, you'd need to evidence this) , and school 1 has new DT studios plus offers additional relevant GCSE options e.g. graphics, engineering etc, whereas your allocated school doesn't. You can talk about pastoral facilities etc too if your child is likely to need these more than average.
The panel can't really agree that your child would e.g. do less well academically at your allocated school, even if that would likely be the case.
It can be helpful to prove that the school has gone over PAN before and coped, but this shouldn't be the whole basis of your case. To simplify, there might be 5 people appealing, and the school has never gone more than 3 over PAN without a bulge class (for example). The panel may agree that 3 additional pupils can be admitted, and admit those with the strongest arguments for the school.
Do you know your position on waiting lists?