The first seven years of life form many of the critical foundations and so choosing the right school now is a great start. If you are not happy with the state school options (and lottery of getting a place) have a look at the private schools nearby. Not all private schools are hot houses.
I went for private as I liked the small classes, facilities, opportunities, lack of necessity to follow the national curriculum and the associated tests (although children have to take the 11+, 13+ if changing school then). The incidental learning was also very powerful, I do have an academic child but the focus wasn’t always purely academic, especially at prep. My daughter didn’t have to do any extra prep to move to senior school and as every other child was moving it was a natural progression.
The fact that teachers have more time with each child helps to ensure your child is understood and supported. The majority of children go to state schools and many many do very well indeed in finding their place in the world. You have already set out what is important to you, have a look at schools to see which is more aligned to you and crucially your child. What the school portrays is what they at least aspire to provide ie if they focus on academia or sport or music that is where the focus is. Enjoy your journey!