I am a grown woman who never knew my dad. He was never involved in my life or cared to be. My mother never had anything but bad things to say about him. Even now I struggle with my feelings on him. What I do know is that it is never a good idea, no matter how big of a loser the biological dad is to talk bad about him to your daughter. His DNA helped to create her, and whether you like him or not, she is part of him. So talk bad about him and you are talking bad about her. She will realize when she is older that he is a loser on her own, but will resent you if you say bad things about him.
Secondly my mother married the first guy that came along and while he tried to be a good dad, wasn't. As a mother, myself, if I were ever in a situation where I were single again, I think I would probably wait until my kids were grown before getting involved with anyone else. If you can not do this, I would not bring men in and out of her life, it will not be a good thing for her on so many levels. She should not know any other man, unless you are marrying him. Pick wisely now, for your daughter's sake, she deserves it, and so do YOU!
And yes, go for the child support, you are going to need it. He should be keeping his pants on if he is not ready to financially and emotionally support a child. My best to you and your daughter. Life is hard, but it is also sweet, enjoy your little girl.