We went through this in 2020. Quite pleased with how it all worked out.
Son was 17 in December 2019. He was put on my wifes (Fiat 500) car insurance for about £20 admin fee. I used this time (2 weeks) to teach him to start & stop.
He bought his own Vauxhall Corsa (sub 1L eco something) in December 2019 and we bought him a batch of lessons. The corsa cost £300 for the year to insure as a learner with no box or anything. Unfortunately due to Covid, everything got stretched out with cancelled lessons and tests. He passed in September 2020. We were charged £500 to cover him fully comp until his insurance renewal in December. So the years insurance cost us £800 for his car.
His renewal came through with 1yrs NCD at £2000 which we were not happy with. My wife shopped around and got it for £800 fully comp.
My boy is on his way to his second years NCD, bought his own car with refereeing money (We pay his insurance as he saves us £80 per month in bus fares for school for him and my daughter). He loves his car, looks after it very well and makes me proud every time i see him in it because he really did show maturity to get it.