Christ,
Going back to original OP ideas,
Our 2 go to a inadequate rated bog standard comprehensive, the likes of OC and others happy describe as failing and not good enough for their kids.
Eldest, just sat final A level, this morning, is shy, but confident in his own way and at the right times, IYSWIM.
So played sport since 4, free, at primary and secondary and out side school too.
Football, cricket, netball (high5's, even though only boy in league at 9-11) and rugby league. Won local schools cricket and netball, at primary and got player of year for both. Played rugby at secondary, National schoolboys champions, in Year 9 2014, and reached final in 2015, lost. Played union from 2016 to this April.
Never cost us more than £4/week, usually less than £100/year.
Did DofE up to silver, only 4 and 2 from this school at bronze then silver. Had to do it with main well off and privileged kids from local market town, 35 miles away. Many from private schools.
He and best mate ended up with 2 extremely privileged, privately educated girls, in a team, ended up doing 6 miles more than other teams as the girls wouldn't go past sheep, cows, in water!
All teams leaders said his best mate and him, where the ones they went to when things needed doing, they did a deal with other girls, boys put up and took down tents and washed up, girls cooked. Also on each night in the cold and rain, those two would, round up all the cooking paraffin stoves and build up mock fire, and tell stories and sing songs to keep every one going.
He was offered two apprenticeships, one welding the other one maintenance fitter, with HNCs. ended up doing A levels. Off to university, in September, 1st in family, not Oxbridge or RG, but top 40.
He is a volunteer Police Cadet, runner up for Cadet of Year, can talk to High Sheriff, Chief and Deputy Chief Constables, also spent 12 hour nights working with kids in care, took 3 on holiday activity weekend, got commendations for how he handled the weekend.
His younger brother does similar,
Both can speak confidently on sport and cadets, and current affairs, both have gone on numerous school trips. But equally, unlike their many of their privately educated peers, they know their weakness, and only talk about it when asked to or when it is relevant to a conversation they are having. They also know from attending such a school, that many have more than them and others have less, but most importantly, every one has something to add/contribute to life
They are used to working in a community, and that community only survives because they all work together, even when some don't want too, so you may need to assist them, possible carry them, because next time, it may be you that needs to be carried. Which is just like the world, they will both end up spending their adult lives in.
So just give your kids a chance to find what they enjoy and are good at. Listen to them. It doesn't have cost £17000 a year.
Also much of the confidence from private schools, is over confidence and/or arrogance. The quietly confident child/adult, who knows what their strengths and weakness are, and are open and kind and helpful to others, will go much further then any know it all.
Finally, money doesn't make people happy, the happiest people I know, are happy in their own skin, and other have little compared to many others, but know exactly what they wanted from life and have got it.