The way I look at it, there can be few other apocalypses more horrifying than grey goo. Imagine, if you will, nanotechnology so advanced, that it ultimately engulfs the entire planet, turning it into a mass of nanomachines floating in space. Even better, imagine such a mass capable of manuevering in space, or at the very least, sending portions of itself out of orbit. Not only would the death of the planet be confirmed, but if there's sentient life anywhere else in the universe, they'll eventually be damned to a grey gooey doom as well.
That said, I think Programming and Biology should be our focus, with the eventual goal of Nanotechnology Killbotics, and possibly some Physics and Chemistry for rocket science.
Programming: Nanobots shenanigans are expensive, and with proper hacking, monetary problems will only be temporary. More importantly though, no self-respecting government will allow you to turn the planet into a cosmic horror. So, the first step is to institute a global conspiracy revolving around brain chips: Programming is significantly more dangerous in a world where brain chips are present. As human brains are not hackable in their biological state, a programmer is unlikely to garner the attention of the government. However, when the world is more or less cybernetic, you can come out of hiding to wreak havoc as you please, and with your skills as developed as they will be, none can properly challenge you. From there, with your mind-controlling abilities, you can work towards a more gooey apocalypse.
Biology: If we're going to bring about a brain chip conspiracy, we'll need some knowledge of biology to properly meld man and machine. Also, conspiracies, though quiet and out of the way, will take a while to come about. Dying of old age is not an option, so finding ways to extend your life through biology will come in handy. Until nano-regeneration is an option, this will be your primary method of keeping alive longer.
Killbotics: Grey Goo. Best end of the universe scenario ever. nuff said.
Physics: If we want to damn not only the Earth, but the universe too, we'll need space travel of some sort. Rocket science, gravitational catapults, magnetic propulsion and the like are necessary for dooming any and all other life out there.
Chemistry: If we take the rocket science method of universal destruction, we'll need both Physics AND Chemistry to make it happen.
SO, with all of this in mind, I saw we'd best start with Programming and move through the sciences in said order. If I'm going to be a man of science, I'd rather not have my work halted by lack of funds or angry world governments. Hacking and a brain chip conspiracy should eventually cure both of those problems.