You could try Scoop, for finance/business news Interest, for general news RNZ.

Sometime Google News works as meta-news source, an interesting headline then use the drop-down to select a source worth reading.  But it's using a bot to crawl the popular sites so often the headlines are much the same as what's on Stuff anyway.  I very much dislike the concept of "personalised news", but you can via personalised settings choose to adjust / add sources and tweak weighting for each source on your personalised Google News page.