I am scared to start a new relationship.?

I am, of last year a single mom of three. Their father has no problem introducing a new girl into my childrens lives. I think this is wrong because he told me she is not "the one". I can't do that. I have to know the person will be there for me and my children. I am afraid of many aspects of this. Mainly my childrens feelings toward this. I am also scared that I will put this new guy first in my life w/o even realizing it. I understand that i am the main example of life for my kids and everything I do will affect them and their choices. I am also afraid that I will be alone, but I am more afraid that I will make a bad choice out of desperation. My childhood did not involve my father enough, in my opinon. My step dad tried to hurt me in a way when I was growing up. Will any man ever treat my kids like they are his own???