I voted for Story Mode first, but that certainly won't happen. There's a highly probability that a demo of the game will be released a couple of weeks (months?) before the full game hits the shelves, so when we get our hands on the final product, we'll already know how the game feels like.
That said, I will do exactly what I did in every single MK I've played, from 1 to 9 = STRAIGHT TO ARCADE MODE WITH SCORPION AND KILL WHOEVER IS IN THE TOP OF THE LADDER. No matter how many tries it takes, that feeling of completing the Arcade Mode for the very first time is overwhelmingly AWESOME.
After that, I'll jump into Story Mode a see what's up with all those new characters. Then trials/challenge tower (if there's one), lab and finally online.
...and I'll probably drop Scorpion that very same day.