Like Felix pointed out, the Academy 1/400 and the Minicraft 1/350 are the front-runners in both scale and accuracy.... but the Academy requires a good deal of scratch-building down in the welldecks. Check out BrianL's build thread that he started here in the "Ships" category. You'll see what needs to go into the 1/400 as you follow along.
I'm 2 years into the Minicraft 1/350. That kit is considered the most accurate on the market so far, yet it still requires a bit of clean-up and further detail.
There are now 2 versions of the Minicraft Titanic: the Centenial kit and the Deluxe kit. The molds were cleaned up so now the windows, electric winches, you name it, now have the detail restored as the kit was when it was first introduced back in the mid 70's. The difference between the two (besides price) is the addition of a few PE details like railings and ratlines included in the Deluxe version.
If you are looking into taking on this ship, my advice is to go with the standard Centenial kit. The money you'll save (instead of going with the Deluxe) can be applied to a complete PE upgrade set from Tom's Model works or Gold Medal Models. I purchased both as they each have different offerings, but most people can get away with choosing just one set. You could also dive deeper into the build and get a set of decks from Scaledecks. It all depends on how insane.. um, I mean intent you are on the finished product.
Also, I highly recommend lurking around over at Titanic-Model.com . That's where you'll find all the info you need to be as accurate as you want, although, some of the guys over there are serious rivet counters. They strive for absolute accuracy....some guys like me, not so much. You'll get some great tips from their online tutorials about the PE stuff and they have a recommended paint chart you can follow.
Oh yeah... the model on the box art of the Centenial version was built by a member of the Titanic-Model.com site and is considered a rock-star over there. His instructions were to build the model out-of-the-box for Minicraft, but you should see his own builds of Titanic and the Queen Mary II. Absolutely stunning work.
Regards, Matt