Okay basically im making a website that has links to other news stories on other sites. So itll be a long list of links to other news stories, is it legal to do this?
I will be using the name of the article on the site and the first few sentences from the story...?
It is legal
Yes it is legal. But let me clear you one thing, It will not get you any benefit. If you are expecting traffic from Google for such kind of news stories, then you are expecting something wrong.
If you want to earn bucks and good traffic, you should start writing original and worthy content.
You won't have any issue in that and as Priya said- start writing your own content, it will really help you a lot.
Its legal, but its prefer if you praphrase the article.