Wonderful story? No. Good story? Yes. Interesting characters? Yes. Although a couple don't have a very big role in the game. Best Tomb Raider ever released? That's subjective. I thought it was but others will say it wasn't
I won't answer the why or why not part because I can't think of ways to explain without giving spoilers. Also I graduated a long time ago and I don't do essays anymore.
It's funny, but I would say that the story and characters (other than Lara) actually aren't all that good. Where this game excels is telling the story of Lara as a character and her character progression. The actual events provide a decent enough setting to adventure within, but don't do anything more than that; i.e. the events aren't that interesting on their own. But I say this is funny, because even though I can recognize this as being the case, I still love the story.
Does it have a wonderful story? No, I don't think so. Like other people have said, the characters are weak. I even think Lara is a pretty weak character. Her "character growth" is kind of shallow, she basically changes from a normal girl who whines into a normal girl who whines less and kills men like rambo. However the character of Lara herself is pretty bland, she doesn't have much of a personality other than whinyness and magical protagonist powers to be always right in every situation.
The writing in this game just isn't very good. It's clearly trying to be a hollywood style action movie, put even Micheal Bay's weaker movies have stronger writing than this thing.
Is it the best Tomb Raider ever? No, I think it's one of the weakest. The gameplay for shooting people is more polished, but everything else takes a backseat. It also treats you like a baby with all of the hand holding, and the exploration is much more limited then past games. In the original Tomb Raider games, you could go almost anyplace you could see... funny how the series has been going backwards in that aspect.