Places for taiwanese to start investing

I’m trying to help my Taiwanese girlfriend get started on some sort of index fund or a low expense mutual fund, but am a bit lost as to where to start. I’ve seen others post about investing at HSBC or Citibank, but at the same time have heard about people having problems at those banks as well. Can anyone recommend a good bank to go to, or any other place where I can help her get started on an index fund?