Displaying user notifications REST API or Streaming API?



I’m creating a website where I plan to retrieve a user’s notifications and display them. The notifications I want to display are times that the user is mentioned in others’ tweets and times the user’s tweets are retweeted/favorited. I want to display these tweets along with the information about who retweeted/favorited the user’s tweet, or who mentioned them. Which API would be better for achieving this goal?