This related question highlights the reason why Admiral Marcus needed Khan's help. But what I'm more interested in is why specifically Khan? There were plenty of other genetically-enhanced individuals as we see
in the torpedo tubes in Star Trek: Into Darkness
whom Marcus could have chosen. So why did he choose Khan specifically?
I'm looking for an in-universe reason; the out-of-universe reason no doubt is that 'Khan is an awesome enemy so we had to include him!'
In the star trek reboot, while in a parallel/alternate universe we know things are the same as prime timeline until the Narada and spock go back into time, essentially creating the point where the timelines diverge.
Because Khan's history is pre-split the reasons in which Admiral Marcus would have chosen Khan is this.
Captain James T. Kirk: [looking at a library picture of Khan on viewscreen] Name: Khan Noonien Singh.
Mr. Spock: From 1992 through 1996, absolute ruler of more than a quarter of your world, from Asia through the Middle East.
Dr. McCoy: The last of the tyrants to be overthrown.
Scott: I must confess, gentlemen. I've always held a sneaking admiration for this one.
Captain James T. Kirk: He was the best of the tyrants and the most dangerous. They were supermen in a sense. Stronger, braver, certainly more ambitious, more daring.
Mr. Spock: Gentlemen, this romanticism about a ruthless dictator is...
Captain James T. Kirk: Mr. Spock, we humans have a streak of barbarism in us. Appalling, but there, nevertheless.
Scott: There were no massacres under his rule.
Mr. Spock: And as little freedom.
Dr. McCoy: No wars until he was attacked.
Mr. Spock: Gentlemen...
[Everyone but Spock laugh]
Captain James T. Kirk: Mr. Spock, you misunderstand us. We can be against him and admire him all at the same time.
Mr. Spock: Illogical.
Captain James T. Kirk: Totally.
In TOS we learn that Khan is a remnant of the eugenics war, and was a genetically altered super human.
In TOS we learn that he was the strongest, bravest, most ambitious, and dangerous, out of all of the tyrants.
We know Admiral Marcus looked up events from this war, and found Khan and his crew, and so logically he would pick their best and brightest, aka Khan.
Because his backstory is based on events from the Eugenics wars, which would not have deviated from the prime timeline yet, we can concur that the things we learned in TOS about Khan from TOS history will still hold as true.
As per the TOS episode "Space Seed" The leader's (Khan) tube was programmed to open first if the ship was found. Khan was the leader so he was automatically the first defrosted. Marcus didn't choose Khan, the cryo tube did :)
