Haven't read all 7 pages of advice, just responding to the initial post:
When I hear "baggage," I think of the person's OWN personal/psychological issues; are THEY dealing with depression, low self-esteem, lack of trust due to bad past relationships, etc. It's not clear from the OP what baggage, if any, this woman has in that sense.
One question you should be asking is what kind of relationship YOU are looking for. It doesn't sound like she's looking for a casual bump and grind and then disappear. Are you? The thing about "committed relationship," of course, is that you can't have a committed relationship in the abstract, you have it WITH someone. So you can't go into a relationship with commitment right from the get-go. You have to date more casually until you get to know each other better, and see if the sense of commitment grows as you go along.
The negatives described in the OP are not her negatives but her family's. So the other question is, how do her family's issues affect her? What is her relationship like with her parents? Is her cancer-suffering father a tower of wisdom and strength to her, or was he a neglectful bastard that she has mixed feelings about, at best? Has her bipolar mother riddled her with issues of low self-esteem or whatever, or is she a loving mom who just has her episodes?
Adversity reveals character. It could well be that she is a model of grace and dignity, dealing with her family's problems with resourcefulness and love. It could be that under the pretty face and the sense of humor is a snake pit of dysfunctionality. If she's the first, she would be an amazing life companion that you would be blessed to have in your life. If the second... not. You won't know until you really get to know her better.
My advice then... you think she's pretty and fun. Go on a date. JUST a date. NOT "start a committed relationship." Just go hang out and have fun and see what happens. Maybe a second date after that. If you still like her and want to spend more time with her, go on a third and keep going. Don't talk about commitment right from the starting line, but don't rule out that it could grow eventually. Don't do anything that gets really emotionally entangled early on, like sleeping with her or going to her father's hospital bed with her. You're not part of the family yet. If red flags pop up and keep popping, step away; if not, you may find that seeing her was the best decision you ever made in your life.