I think my advice would be to save as much as you can in each adults ISA & make sure you both have a reasonable pension provision.
After that, maybe save into an ISA or such for the DC, but with the bulk of savings in your own names for reasons given earlier.
Ours are older, 16 & 18, but we have managed to save a decent amount in our own ISAs and also some into Isas for them. We part paid for driving lessons for eldest as his 17th birthday & xmas presents (he contributed earlier birthday/xmas money that he had saved), we bought a small car but he insured it from part-time earnings. Without the car, we were having to ferry him to work at weekends and look after my sick mum 70miles away, so it helped us.
He is now at uni, he gets minimum maintenance loan, we give him the top-up to cover hall fees and a decent monthly allowance (not over the top but enough to live on). He has also saved from his wages, so we know he doesn't waste money. We are fortunate that we were in our 30s when we met, married, had kids, so both had careers and houses bought in early 20s. We are thus comfortable enough to help now.
We had also planned to help with money for a house deposit, assuming we didnt have any life changing events, but our DC have recently inherited some money from a cousin of mine, which has now removed that need. We may still give them a bit extra, depends where they end up and how much property is, but that is now more optional.
One thing I would say, is use the time between now and 18 to instil some money values, show them that you are saving and where, encourage them to get a job when old enough, etc. My DS received his inheritence just after he turned 18 last year, it could have been disastrous, but wasn't. He was already careful with money, we had encouraged him to work, save some, spend some, etc. The inheritence has also allowed him to get more involved in his Stocks and Share ISA, choose funds, watch progress etc. Unless he changes completely at uni, I know he will go out into the wider world with some good money sense. We are now instilling similar values in DD.
One last word of advice, how much you help your DC depends only on your wishes and your financial situation. Asking, is it too much, not enough, is like asking how long is a piece of string!! If you can afford it and want to do it, then do it. Ignore any well meaning advise. One of my friends was aghast that we bought DS a car - despite her spending lots on prep school so her DDs could then get into grammar school. I politely told her I could spend my money as I wished, as she did hers.