I think Amber was the right choice. I think that it's easier to kick an addiction than to change your entire personality.
1) she set up the Zydrate Support Network, so that shows initiative and leadership
2) she showed she can get people to do what she wants without having to use violence

I think that Luigi's temper is too hard for him to overcome (a company with a head that keeps openly killing employees and others?) and Pavi is too selfish and vain and too focused on getting his own pleasures.

That's a very accurate view.

Honestly, I don't think that any of the Largos are worthy of running GeneCo. Amber would be the better choice out of all three of them, but in the scheme of things, I think that someone with no addiction/anger/vanity problems should run the company.

As a rabid Luigi fangirl, I have to suggest Luigi.
Amber's a spoiled attention whore that's never worked a day in her life, and now she has unadulterated access to the Zydrate? She's not a businessy type, she wants to be in the spotlight.
I don't really think Pavi has would take it, either. Why does he even want it? Company CEO doesn't sound like his kind of thing.
Luigi, on the other hand, was first born. Technically, it should be his, and as being first born, Rotti probably expected him to take over the company and raised him as such. Plus, he's determined and I expect he would expand GeneCo from company to the corporation with complete control over the economy. Only problem is his temper, and without anyone to answer to, there'd be a lot fewer GENterns running around, but that's a local thing; GeneCo is global. Not to mention that GeneCo is essentially the government, and who would stop him?

Well, Amber's probably the smartest and most "responsible" one of them, so yeah, she's the best choice.