I think it all depends. I do think BPD carried a large stigma, which is unfortunate. But I have worked with several classmates, co-inters and co-fellows that have clear Borderline organization / PD.... they were all smart, well-intended, good clinicians and dealt with issues as they came up. I do think I would be careful to disclose that right away because people will start to go back to their stereotypes about BPD and will look for any information that confirms those stereotypes.... I think the number one thing you can do is obviously continue to seek treatment for yourself, more than for your career or related to your father. The rest will fall into place, academic, career and so on...
I disagree though with revealing personal reasons for going into the field being a total kiss of death. Like someone else said, we all became psychologists for a reason... and it's usually not because everything was totally hunky dory our entire lives ;-) I have found that some supervisors are much more open than others. I was asked why/how I ended up in the field, my motivation for it etc., and I gave pretty much the whole story from A-Z. Though, I will say my story doesn't carry that much intrinsic stigma.... I still got a APA internship and an APPIC postdoc, so it cant be that bad to disclose to a certain extent. I think the KEY is sharing - but with some limits. You don't have to label yourself as Borderline. There IS such a thing as an overshare, however... regardless if it's your diagnosis or trauma or other things going on... and you have to exercise good judgment about what to reveal, when, and how. But, it should not be a black and white, yes/no sort of decision making process (how apropros for BPD).