To first contract? I'm not sure what you mean by that.
When talking with a client for during pre-negotiations you want to come across as confident, but stop short of arrogance. This part has to be handled with care, but make them feel like they're nothing special (although don't directly say anything of the sort). Even if you don't have any other leads at the time, don't let them on to that. They should have the feeling that a lowball offer will get met with a notice that you're on a different project and no longer interested in theirs. If they get the feeling that you're desperate they'll eat you alive.
As VG says, you need to be confident of yourself and your abilities. One way to do that is by entering the meeting prepared. What that preparation requires will depend on what you do, but expect that you will need to give answers to a few basic questions and that fumbling those answers may come across as evidence of your inexperience.