First, let me express my sadness at hearing of your difficult family history and the deep respect I have for the work you have done to bring yourself to a place where you are ready to look toward marriage. The questions you ask are deeply personal, and I will do my best to offer guidance from Jewish tradition to encourage you to move forward in your search for a life partner.
Very directly, I do not think you should “just throw up my hands, tell myself I am not fit to marry, and just live for work.” The very fact that you now feel ready to date for marriage is proof enough that this is the direction your heart and soul are leading you in, and to deny that would be to deny an intrinsic part of yourself.
The Torah tells us, It is not good for the Human to be alone (Genesis 2:18), establishing the basic need for all people to have companionship. I believe it is precisely that need that you are feeling now as you consider marrying – the desire to have another person in your life who will love you and to whom you can give your love. That need is hard-wired in your soul, and to deny the longing that you clearly feel would almost certainly inflict a great deal of suffering upon yourself.
While I know that certain specific Jewish communities do scrutinize family background, outside of those particular communities I don’t believe Jewish women are any more particular about their potential partners’ family histories than non-Jewish women. In my community, there are many people who were orphaned, children of divorced parents, or who suffered abuse, and despite the apparent difficulties in their background found wonderful loving partners; I believe the same will be true for you, so long as you have the courage to continue moving forward in the face of your fears.
The right woman for you will love you not despite your family background, but with it and even because of it – because no matter how you grew up, you have done your own work to become the person you are today. And since the fact that you are asking this question suggests that one of the qualities that you value in a partner is a shared engagement with Judaism, I would encourage you to honor your personal values and seek a Jewish partner for marriage.
The question of whether you “can be a decent spouse and parent and fulfill the obligations to a family” is a question that almost every person – no matter what his or her family history may be – faces at some point. There is no reason to think that your personal history makes you any less qualified to be a “decent spouse;” that will be determined not by your past, but by your present and your future.
You are more than the accumulation of your past history; you are a beautiful soul, created in God’s Image, and deserving of love and companionship. I encourage you to be brave and seek the loving family you desire.