I would say go for Warwick Prep if you want private school to be worth it. It is a phenomenal school and the factory reputation isn't accurate, it just tries to help kids get to their potential. The extra curriculars are very impressive and the foundation schools it feeds into keep flourishing. It is by far the strongest primary school.
Kingsley is a good school but has never pushed academically. Even though it has been taken over by the warwick schools foundation (essentially by warwick prep/kings high/warwick), the rumours I heard is that it is essentially going to be the more pastorally kind school and cover their sen children. It has always has the reputation of being less rigorous at secondary. However, the move to co-ed is a huge change.
Arnold Lodge has always been good for prep, but has floundered a little on an identity for secondary. It is meant to be quite well rounded and kids seem nice.
There are some other really nice schools in the area - Crackley Hall is the feeder for Princesthorpe. Bilton Grange (similar to Warwick Prep) - feeds into Rugby school. There are so many strong private primary schools in Warwickshire, each a little different, so worth googling.
A school I would 100% check out if you want gentle, pastoral, but kids reaching potential would be The Croft. It hasn't been financially secure in decades, but is meant to be the nicest environment of any of the prep schools locally. If your child needs a supportive environment, Sibford is phenomenal - and trying to move into a more general school rather than SEN school. I have heard really good things.