According to the FAQ in Steam Discussions, Angels are gained by lifetime earnings:
Q: How do you get angel investors?
A: Your Angel Investor total directly correlates to your all time cash earned. To receive the bonus from your angel investors, you must redeem them by performing a reset to gain angel investors.
Q: Is there a formula for earning angel investors?
A: [150 * the square root of (your all time cash earned in quadrillions)] – AI spent. This means that when you earn an angel investor, it takes more money for you to earn your next one.
tl;dr
For a "good enough" optimization, buy cash upgrades as soon as you can and angel upgrades as soon as they are "safe", meaning the game does not pop up an "are you sure?" box. For more in depth optimization, do the math to figure out whether investing in more businesses (to reach the unlocks based on having a certain number of businesses), your main moneymaker business (to slowly increase profit), or specific upgrades will increase your current profit the most.
Cash Upgrades
As Unionhawk pointed out, upgrades apply to all current and future profits and it is generally a good idea to buy these as soon as you can. With that said, you also need to consider the opportunity costs of these upgrades vs buying additional businesses.
For example, let's say you need to buy 10 more newspapers to unlock the next "unlock all" achievement. For a similar cash price, you could buy an upgrade that affects only lemonade stands. Eventually you will buy both, but which one will increase your profits faster?
If the lemonade stand is your main money maker (you can find this out by looking at the money per second once you have that upgrade, otherwise you can estimate it by the amount of profit the business generates divided by the time it takes to generate that profit. You don't need to be 100% accurate as usually the "best" business is many times more profitable than the others, sometimes even tens or hundreds of times), then buying the lemonade stand only upgrade might make more sense than the "unlock all." But if a different business is currently your most profitable, then the "unlock all" makes more sense as it will increase that business's profits and help you earn your money back more quickly.
The best business, in terms of profit per second, hops around depending on what upgrades and unlocks you've done so far. I'm fairly late game now (hundreds of novemvigintillion angels, 3790 newspapers) and donut shops pull in 3 times what everything else does. A few restarts ago, newspapers were pulling most of the profits. Much longer back, lemonade stands and oil companies were the best. The point of this is that you can't always assume that business X will always be your primary moneymaker.
Angel Upgrades
"Safe" Angel upgrades are almost always a good deal to buy immediately. The game considers a "safe upgrade" to be one that requires less than 1% of your total angels. Each angel boosts your profits by a certain percentage (the percentage eventually peaks at 30%, on the mobile version at least), so there is some math involved to determine if spending X angels to boost profits by Y makes financial sense. The safe rule by the game is a great starting point, but you can run the math to determine if an unsafe upgrade would still make you more money.
Best Answer
It applies immediately. You'll see in the investors menu that the Bonus per Angel is increased by 2%. The upgrade is reset (just like all upgrades) when you reset the game to get more investors.
I am not sure what the percentage bonus is before you buy it, but I think it is 5%. So you'll get from 5% bonus to 7%. That means the minimal amount of investors to purchase this upgrade is 350.000. (350.000 * 5% = 1.750.000 % bonus, 250.000 * 7% = 1.750.000% bonus)