Facebook Privacy Questions?

[Sasos]

I want to create a facebook account and I know this sounds odd, but I want to make sure that nobody knows I exist on FB unless I want them to...(There are some people that I do not want knowing that I am on FB).

Basically, I understand that there are some privacy settings like people not being able to see your pictures/bio etc.
But I need to know if I can be seen via other methods (Ie. - a random person is looking at somebody's friend list and finds my account and then knows i'm on FB. Or if I became friends with somebody it came up on their wall "X is now friends with Y" with my name, showing my name to potentially anyone.

I know that this question is slightly stupid - wanting to become unknown on a social networking site...but I need answers!