I would recommend playing Last of Us 1 just so you can play the story, live the characters and learn what they are like as people.
Do you need to play the 1st one though? Not really as the start re-tells what happened at the end of the first one and why it happened that way. Good way to bring new gamers in to this game.
I have not got too far in to it, but WOW! I was waiting for the gameplay to start from the cutscene, oh wait, they look the same?! haha, me waiting there not knowing.
Love the storyline so far, the characters (old and new), the way the game plays and the graphics.
I can see the storyline opening up a lot more but I am very interested to find out how this will play out
This is the kind of game will tell you how it is, but NEVER ANY SPOILERS as you just need to play it for yourself.