I am to a large extent with petticoat and others.
I am sometimes amused here on MN where posters spout on about things at their DCs school that they could only actually really know to be true if they were 7 years old and sitting in that classroom in ankle socks! SO much of what we think we know about a school is gleaned from the edited version our DCs tell us, 3rd hand accounts from other similar mums, playground gossip and scuttlebutt, often told by mums who don't allow their lack of actual access to the classroom get in the way of their story!
I think when it comes to school selection, wise words have already been said here. A quick tour of the school on one day really won't tell you exactly how your DC is going to 'fit in' at a given school, 'gut instinct' or not, especially, dare I say if there's a PR machine at work! You could view a happy, productive classroom full of directed activity and lots of studious little girls and think 'I want that for DD', whereas she ends up in the class next door with the teacher whose forte is keeping a bit of a lid on the wild exuberance of that cohort of boys, for instance. Yes, if chairs are actively flying through the air, unchecked, you may well be right in avoiding that school, but you have to be there at that moment to see it!
The 'best' idea is to talk to trusted mum-friends at the school gate about whether their DC is happy there- and a quick look at the cover letter of the OFSTED. And look at the kids as they leave school with their families. Do you like what you see; everyday, normal parents wandering out asking their DC about their day or 2 mums grappling in the mud pulling out each other's hair extensions?!
- though I once saw that at my DCs first juniors!
And Heads come and go, state and private. Everything can change in a term.
FWIW I have a work mate who feels she has made a mistake re education. She has one DC, a DD of now 9. She was apparently happy and achieving reasonably at the local state primary in a leafy village in posh Hampshire. Her mother believes the DD to be 'very clever' and 'sensitive'. The father is a bit neurotic, to be honest! The DD was having difficulties with one particular boy (the father loathes boys, esp near his DD!). The school rearranged the classroom to accommodate this, but this wasn't good enough, so she was whipped out and sent to a ££ academic prep. She is now being constantly, subtly bullied every day by the girls at this school as they are all way more 'alpha' than her but it's a small class so there are only 7 girls in it so the D has nowhere to go to, as it were (the downside of small schools). The mother is going to move her back to the village primary but it's currently full. The mum has also recognised that for a DD like hers, once private, always private as she did see that 4-7 years spent in a small, 'nurturing' indie wasn't really good preparation for 280 DC entry state comps, even though they're amongst the best in the country, academically. ( I know you were talking about a friend when you mentioned private prep as a stepping stone to state grammar but believe me, state grammars can be challenging and alpha, too! Despite what many think, they're not a direct substitute for private secondary!)
I am not entirely sure we have picked the right secondary for DS2, though, ironically, we picked it for him when it was DS1's turn to go 2 years ago! DS1 is reasonably clever and would be fine at most of the local secondaries as he would be in the top or next set where, frankly, behaviour tends to be better; DS2 will be in the middle or set below middle. The school is very MC so my hope is that, from what I've seen and experienced (DS1 is in Y8 there now), DS2's classes will also be reasonably well disciplined as well as all the DCs arrive being 'school ready'. But I do worry that the school rests heavily on its stellar academic results and that the 'less able' might not get the focused 'look in' they might get in a more broadly spread comp (like our second choice was!). However, nothing is writ in stone so I shall see how it goes for Y7 come September.
Final thing, again, as already said- your DD will change beyond recognition in the next few years. And our perception of what they can handle. DS2 is almost 11 and small (and young!) for his age. He started Scouts the week before Easter, having been 'in' since Beavers. Bloody hell, it was mayhem in there! He only knew one boy who is an old friend so that was OK. I confess I was unsure about leaving him as the place was heaving with 12-14 year old boys turning into men, whooping, shouting, running, bundling.
Anyway, I picked him up and I asked how he'd managed and that he could consider looking at DS1's Scout Troop (different village, long story!) if he thought it was too boisterous; but he looked non-plussed at me. Why would he want to try another one as this one was fine and he'd had fun..?!