Everything everyone else has said but I'd also say you need to inspire in your children an independent streak. They have to want to break out of their groove and from the herd.
DH's granddad was a miner - sent down the mine on his 14th birthday. His teacher went to the house and begged his parents to let him stay at school because he was such a clever boy but he was the eldest of 10. On his 18th birthday he left the house and instead of going to work he went to Cardiff and joined the army.
He broke out; his brothers and sisters and their children still moan about the impact of the mines closing. They could have broken out too but they didn't have the confidence or independence to do it.
Interestingly I don't think it is always about money. I am from a quite wealthy farming family. I was probably the last of the generation where there wasn't a great expectation to go to university, especially for girls, where nobody much cared about O'Levels, where you could still get a good City job without a degree if you knew the right people, where lots of girls did a secretarial course and a cordon bleu cookery course, etc. Shuddersome now. But all of my family were well educated and well travelled.
Sometimes I think the emphasis on qualifications and degrees has become extraordinary. Even DH's granddad who left school at 14 was incredibly well read and well educated, wrote well and was ace at arithmetic. I see so often job applications from young people who have, sometimes two Masters degrees, and they can't write well, and sometimes those who do get to interview have no idea how to present themselves and speak in a clear and articulate way. I once interviewed someone, albeit for an entry level job, and throughout the interview they said "you know" 47 times - after the first question I started marking fives.