Will fallout 4 continue in the story of fallout 3 Or will it be a completely new story

No, fallout nv doesnot continue the story of falllout 3. Instead it has another great story. Fallout nvs story is that you get shot in the good springs cemetery benny who is a high social leveled guy who stays at the tops. In the entire story you try to track down Benny and his gang.you have many options of who to trust.one of my favorite ways is to go w/ the ncr and reunite them with the boomers,brotherhood of steel,and the groups of new vegas strip including the kings from freeside.from the fallout 3 game they did bring back the brotherhood of steel.they are hiiden ubderground in bunkers. thats my answer and i hope it helps you.