You should put the grammar school first if that's your preferred choice. At the appeals, the panel might be interested to know what your choices were and if you put it as 4th then it gives them the impression that you prefer the comprehensive schools over the gs.
You must state the grounds of your appeal for e.g non-qualification and oversubscription. You can highlight the fact that your dd was not even given the opportunity to pass via HTA (or second chance) due to the lack of cooperation, support and interest by the ht and primary school. You can turn this into something positive so it may well work to your advantage. Compare a case that didn't go to a HTA at all, as opposed to one that did go to HTA but eventually failed the HTA.
The panel also may be interested in whether your dd was (over) tutored or not. The fact that she passed overall Maths and English without any tutoring is a plus.
They will likely focus on her weak subject which in this case is non verbal. So make sure you have good reasons to justify the brief shortfall in marks. Explain to the panel she just needed 2 or 3 more questions to pass, really. Downplay her weak areas but focus on her strong subjects - say all the positive things about her Maths, English and her overall academic ability.
Before Easter you'll need to start collating alternative academic evidence: supporting letter from HT, supporting letter from teacher, CATS scores (if any), predicted SATS scores (or new systems levels). Other docs - medical/social evidence, distance to school (maps, bus timetables) etc.
Research the appeals history/stats of the school over the past few years so you'll have an idea of what are your chances of winning.