We looked over 3 schools the first time and another 3 the second time, but were restricted in our actual choice due to need for disabled access.
Went with the dc and had a joint family discussion.
Out of those schools, we saw one on each occasion that we would have been anxious to avoid at any cost:
the first one was run by a religious, sect, really disorganised, had no idea how they would arrange disabled access or pastoral care, spoke as if all parents would find academic subjects nasty and threatening and something for the school to protect them from insofar as possible
second school equally disorganised, conflicting info on pastoral care or special needs, teachers who showed us round also seemed very reluctant to speak about the more academic subjects
All the other schools we would have been ok with.
As for the personality of the headteacher, there are things I would be wary of: one that speaks with no empathy of struggling or disabled students or students with learning difficulties I would give a wide berth (we've dealt with one of those in the past and it really affected the way the whole staff behaved).