Which NSA watchlist are you likely to be on?
What's the cheapest way to destroy humanity?
When you have $ 1 billion, you can kill a serious number of people by grabbing an asteroid and hurling it to Earth.
Hitting land would likely cause an extinction level event. Hitting water would wipe out almost all of the coastal population (and likely trigger an event at the extinction level too). I'm torn as to what would kill more people.
Hitting Earth is a little tricky, especially when the asteroid you have selected takes a lot of fuel to leave orbit and you have little fuel to bring it back to Earth. I think it can be done within budget. With current technology, this is certainly doable if the budget is unlimited.
An alternative is to patiently wait for a very large comet to fly by, grab that comet, and throw it to Earth. Simply select a shape from a table conveniently compiled by NASA:
Since the comet is already headed for Earth and has a non-zero chance of hitting Earth, it would likely cost less fuel to nudge it just to get it to Earth.
Now let's discuss the cost. India has managed to send a $ 74 million probe to Mars. I think so far this is the cheapest that anyone has ever done. The Beagle 2 cost the British 120 million. So sending a spacecraft just slightly beyond Mars (or less than Mars in the case of comets) would definitely be in the range of a $ 1 billion budget.
One advantage of a kinetic projectile is that it is a purely physical process. You cannot develop antibodies or antidotes to an explosion or a tsunami.
The other benefit is that it is likely to cause massive climate change. This, in turn, leads to crop failures leading to more deaths from starvation.
Defense / counter defense
Of course, if you can do this, the governments of the world can use similar technology on a similar budget to nudge your asteroid / comet so it doesn't hit Earth. But anything defensive has to be done pretty quickly because the closer the stone is to the earth, the more fuel it would take to get it out of the way. (BTW, if they do decide to destroy it, they are doing you a favor by increasing the number of impactors.)
Here, a simple counter-defense would simply be misinformation. Infiltrate either NASA, ESA etc and post misleading statistics showing the rock would not hit earth or send false messages.
You can also try to be sneaky. NASA constantly tries to monitor approaches at close range, but every now and then they manage to spot the comet just days before the approach. This is not enough time to start a defense. Of course, if you go this route you shouldn't choose a comet from NASA's list of comets.
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