I think the British government is sensible in not allowing people to drive until they're 18. In fact, sometimes even 18 is a little young.
British Government and sensible in the same sentence without the word 'not'? Now that's unusual.
But I do agree with you, 18 seems to be a good age to start. Though you're allowed to start learning from the age of 17 in the UK, which even though it's only one year, seems to make a large difference. I'd say bump it up to 18 and keep it at that.
Putting it any higher would be ridiculous - no matter how high you put it, you're still going to get irresponsible drivers, and it will have an effect on how potentially employable young people are.
I'm 20 and started learning when I was 18, which worked out nicely as it gave me independence when I needed it - it also means I can work, as there's no work within walking distance where I live and public transport is next to useless. I'd be lost without my car (which isn't anything fancy, a T Reg Peugeot 306 if you're wondering).
Back on topic, for a first car I'd go for the cheapest thing you can find that's reliable. Not stupidly cheap where you know it's not going to last long, but find a mid-point. In UK currency i'd say look at spending around £1000.