In both cases I was looking above all for the school where they, and I, felt they would be happy. I didn't particularly bother about sports etc facilities, we were primarily looking at London selective indies and they all offer amazing extra curricular activities and facilities. My oldest DD is a Science geek and wanted to see the Science labs (I wouldn't know one from another ) my younger DD is a drama queen but that said, she didn't pick the school with the best facilities. I didn't particularly worry about academic results because though local parents have a notional league table in their Heads, the reality is that all the schools we were looking at enable bright DCs to get strings of A/A* and to the best universities.
We did look at state schools, the local ones and the super selective. We were attracted by the social mix in the local outstanding comprehensives but the non selective ones are hugely oversubscribed and we were going to have to make a late application. We did not get offered a place in a local school initially and when we did, three weeks into term my DD was settled elsewhere. My DD hated the super selective because the staff were extremely cold (perhaps not surprisingly since they have 10 applicants for every place) and openly stated that they expected those who came bottom in yearly exams to leave. That didn't make DD feel as if they had any interest in or care for individuals, and on top of that the Science labs were limited and dingy. She said it felt a bleak depressing place. She did manage to get into the required top 3 percentile in the admissions test but completely refused to go there.
It was during the admissions process that she finally realised where she wanted to go, and it wasn't the most selective school she was offered a place at. She found them arrogant and patronising during the interviews whereas at the school she choose she clicked with the Headmistress. It was not just that interest was shown in her and her experiences overseas but that it was done in a way that was intellectually challenging but also with a sense of humour and fun. Another school that offered her a place sent the wrong exam paper overseas and then insisted she sat the right one when back for interviews so she wasn't impressed by them either!
Sadly come DD2s admissions process all she wanted was to get selected for the same school as her sister. She does not find it as easy to show her ability as her sister, though in some areas she actually has greater ability, and she had a diagnosis of SpLDs so we were looking for schools with good support, and that showed their commitment by giving extra time. She did get offered a place at her sister's school and accepted it, though I just felt that another school would be better for her, one that was coed (she doesn't handle girly politics well) and (slightly) more mixed academically. I even had dream about it. And that is where she choose to go at 16 after coping with a very difficult cohort, and exclusive and manipulative behaviour at the other school for 5 years. She is very happy, popular and doing very well academically.
So there it is, a combination of the practical and the intangible, that the schools just "felt right" .