How much should I save before living on my own?

I currently live with relatives and I have a full time job. I want to save $30,000 dollars in about two years time (with a cushion of $14,000 in the meantime for emergency and necessity funds) before I go somewhere, but I would like to move sooner if possible, I just want to make sure I never have to go back. I wanted to save a lot because I didn't want to leave anything in chance.

I don't want very much out of life. Just to live alone and write stories. I can sacrifice having the internet for a long time if necessary, and I'd live off of just top ramen and water. I'd want to live in a cheap studio apartment somewhere secure and never have guests or visitors. I don't care where I have to work or live as long as I can do those things. I don't have very much, all my belongings fit in my car, and I'd only get luxury items very rarely (usually something very cheap; a book or a DVD, etc.)

Would this saving/moving plan work for me?