Hold on fellow survivor, relief is coming, including a relationship that will get you what you want, support and loving care. I personally find talking to the eyes as a way to stay present, not to be launched into the past where I needed to please or I would be abandoned. Please consider finding what you like in this girl, a friendly trait such as if she is into sports, then you like her being into sports. Talk to that, sports, exercise, being fit and healthy. If she is active in music, charities or banking, find what you are comfortable with in those areas and be with the "friend". Make sure you mention your passions as well, and if she has any knowledge/interest in them. That may be a good time to interject something about supporting abuse survivors without sharing the whole story.
You are a healthy guy who is looking for an equal, someone who can support you in your goals and who can support a partner in her goals so that both of you are successful. If you find yourself feeling like a second class citizen, take a moment and ask yourself why "in the present" you are feeling this way. You will discern your triggers and can move to center and ground yourself, leaving yourself more room to be aware of how you are feeling and acting.
Most importantly, the worry is worse than the activity. We cannot do anything while we worry, but we can take action to make sure the activity is moving the way everyone involved wants it to go. We are good that way, we can work in a group to a common goal and be successful, even if that group is a two.
Much success to you king, I am looking forward to your sharing how you date went, make sure afterwards that you consider if she could be the right one or if indeed, she is just another pretty face ;),