Am a parent who has just gone through this this year (and thankfully got my first choice!). There is definitely a lot to be said about gut feeling.
What would have been our first choice originally was knocked out of contention after the tour. Everything looked a bit sad and tired, the children were unruly and the head looked exhausted and was saying that they had no money as she took us round.
We ended up putting our catchment school (originally not on our list, as, historically it hadn't been great...until a new head came.on board 7 years ago and really made a huge difference) after going to see it just in case. It was like night and day- the head was clearly very proud and inspirational, the walls were full of kids work, the kids were super happy. We were allowed to wander the school and ask questions of anyone (it was one of two open days where the head gave a spiel at the start, and then said that they had nothing to hide, so we should explore). The year 6s, governors and teachers on hand to help were genuinely enthusiastic about the school and both my husband and I left feeling like it would fit DD perfectly.
Both schools were rated 'good' by OFSTED, but the energy was totally different once you looked beneath the surface.i know that my heart would have sunk if we'd opened the email to find the first school; instead, we opened a bottle of fizz when we got the second!
I guess what I am saying is to look at a wide variety of schools, as things vary hugely and you don't always know what you need until you see it. (Also consult local Facebook groups- our local one was the reason we went to see school 2, as there was so much positive feedback).