I honestly didn't think dd was anything different at that age, I just thought it was a combination of her interests, normal range brightness, and appearing unusual just because her peers were mainly lower achieving. Plus she was similar to friends ds, who I now realise was also an outlier, but at the time I just assumed was normal like dd.
My criteria was simply the usual pastoral and atmosphere stuff, along with evidence they differentiated across the ability range. The sats results for dd's before she joined were below average. But broken down were spread across the entire range, and with the above average sen and fsm indicated a willingness to differentiate for the individual, not just pitch to average and overlook either side. If I'd simply chosen the outstanding primary with high sats, with the hope she'd find equal peers and be able to access resources from higher years, she'd have been screwed because she'd have quickly exhausted those resources. And wouldn't have found peers on her level there either. Instead at a school most mumsnetters would run screaming from, she benefitted from the attitude that dc all have differing needs that should be met. And trying to accommodate her was done in the same way they were used to accommodating extreme outliers at the other end, because they were practiced at differentiation, even that which went beyond what could be done within a group lesson.
However, I still think if I'd gone in with the attitude that my dd was amazingly gifted and the class teacher would struggle to meet her needs, it would naturally have insulted the staff and ruined the relationship. So instead of casually telling me they were doing x now because they couldn't just differentiate in lessons, or in passing mentioning that they were doing y because in one subject she was beyond any of the primary staff available, I'd have had a load of staff working from the view I was a deluded nutter until proven otherwise instead of the open minded approach they had. I also don't think that when we had issues with a y1 teacher (crap across the board not just dd) or the v occasional supply that it would have been resolved as quickly if I had the rep of being that parent.
And at schools where they really can't be arsed with the most able, no amount of demanding or telling them your childs capabilities changes anything.