I guess the best "age" would be where one is legal for all things necessary to take care of one's self (can get credit cards, car insurance, etc.) and where one won't get unduly hassled about one's age.

I moved out about six months after I graduated from college, I had a job and car and credit cards and my stepmother was getting on my nerves more than was healthy :-) I found a house-sharing situation, little house in a good neighborhood of the big city.