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My half-sister suddenly reached out to me - what should I do?

My half-sister suddenly reached out to me - what should I do?

I have a number of half-siblings that my father had from different women at different points in his life, so it wasn't much a surprise for me.

However, one of them reached out last month because she was moving nearby with her boyfriend and she thought it would be nice to connect. She also reached out to my full sister but she apparently she had no interest in a relationship.

I was a bit cautious at first, I had really seen her only a couple of times (one being my father's funeral) but she was friendly and seemed genuine so I gave it a chance. First we texted for some days, then met up a couple of times - we also made projects for New Year's Eve, both my wife and my mother are fine with that and they met her once.

One of the best things is that we have a lot of interests in common (blood is thicker than water after all) especially regarding cars and outdoor life. Sometimes we talk about our father and it left me a bitter taste to learn that she was raised by her grandmother because her mom died when she was little and my father kept his distance.

Now, I do have the intention to nurture a familial relationship with her, but I'm not sure how to navigate this - I spent a lot of my life complaining about my father neglecting me, but this girl was pretty much abandoned. She's not resentful or anything like that though, and she took our sister ghosting her in stride.

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Over a beer I bluntly asked her why she waited our father's death before reconnecting (although we were already friends on Facebook) and she said that my father never wanted for us to interact - which, knowing my father, it's true as he used "divide et impera" with his children; and after his death, she got cold feet a couple of times.

I also bluntly asked if she looked me or my sister out for other "reasons", and she took it well, she said my concern is legit but she's not after money...
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... or favors and hopes her actions will show that.

Insofar I have no reason to not trust her as her actions match with her words and her profession and personal life are one of woman who has clear and noble life goals and a good person overall.
My wife too agrees with my opinion and I trust her opinion since she's usually good at characterizing people.
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Almost a year later after asking this question, I can assure that things are very good between us and my sister and her partner are officially part of my family.
We have already made plans for Christmas and New Year.
My half-sister suddenly reached out to me - what should I do?
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