Displaying user notifications - REST API or Streaming API?

restapi
api

#1

I’m creating a website and want to retrieve a user’s notifications and display them. The notifications I’m wanting 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?