I have looked at Private schools, although my kids are State.
The school that impressed us most had a very clearly defined ethos, and didn't hide from proclaiming it enthusiastically even if it put some parents off (actually the same has impressed me about some state schools).
Other things I have liked: class size, facilities, friendliness of staff, staff who on open days can talk to my kids and my kids like (my son quite liked one girls school because of the teachers), pastoral/spiritual side (I liked a Catholic school's Chapel and Chaplain). I have also been impressed by one school which doesn't charge extra for TA help, the car park of one (they had actually thought about the safety of pick up and drop off), and the library and librarian.
Things that have put me off: pretending that strategies copied from the State system are new, shocking low Oxbridge from selective schools (if you are selective I expect much better than the local State school), selecting at 4 and giving the impression they will be continuing to 18 then be the Oxbridge candidates, just being academic.
Scaremongering would put me off.
The more opportunities on offer the better. The more they can take away the stress of parenthood the better, eg. ballet lessons in school, prep clubs. Information on how they handle things if things go wrong, the idea of partnership. Those kinds of things are also attractive. Any unique opportunities should also be flagged (eg. marching in the Lord Mayor's parade in London).
Hope this helps a bit.