I haven't had much luck trying to destroy assets to affect stock prices either. But here's what's been working for me so far. It's not a guaranteed quick-billion but over time you'll get there.
Invest in Debonaire!
The stock price for Debonaire consistently fluctuates between around 4.8 and 7.4 (at least from what I've seen in my ~60 hours of story mode gameplay). Since the price is so low, that tiny change is actually a significant percentage. If you invest everything in the stock when you see it anywhere below 6 or so and then sell it back any time it goes over 7, you're making a decent percentage (up to 54%!) back on your investment at a relatively frequent interval.
If you are actually trying to reach $1,000,000,000 then this method is going to take a long time. There's probably something better out there. But at least it's something reliable to do until someone finds that better thing.
As for precisely how long, given your starting balance of 26 million and assuming an average ROI of 10% (YMMV) and ZERO extra spending, you'll have to invest and sell everything 39 times to reach a billion dollars. But only 19 times to afford the golf course.
The Jewel Store Job
The maximum take for the mission is $4,946,153 if the player smashes all 20 displays and chooses a good gunman. $2,500,000 will then go to Martin Madrazo while the rest gets split between the crew.
The Merryweather Heist
No payoff - Reason is spoiler
The Paleto Score
The crew manage to get around $8,016,020 during this heist.
The Buraeu Raid
no payoff
The Big Score
Choosing the obvious approach will yield around $31,000,000 per character, as long as you choose a good driver to pilot the helicopter, otherwise half the score will be lost. Taking this approach is far more difficult.
Choosing the subtle approach will yield around $24,000,000 per character. It is important to have a good hacker; lesser skilled hackers will cause lag in the traffic lights making this part of the heist more difficult.
Good Recommendation
solarosh
On a side note, I recommended only doing the first Lester mission for now. Reason being, these missions biggest payoff is in taking advantage of your advance knowledge of the repercussions these missions have on the stock market. Doing so is some of the best money in the game, and logic dictates that the more cash you have on hand to invest before rigging the market, the higher the dividends you will reap... Remember -- Always Buy low, Sell high
Sources
http://gta.wikia.com/Heists
http://www.ign.com/wikis/gta-5/Blitz_Play (solarosh recommendation)
Best Answer
Pretty sure the only "armored vehicles" attainable in single player are the Rhino tank and the Duke O'Death (DoD is only available to "returning players" and those lucky enough to actually spawn the "Duel" random event and get away with the car). You can't even buy the stock Karuma (non-armored) in story mode.