It's (mostly) a tradeoff of time, investment size, and risk/type of risk. Your investment strategy also determines your lifestyle to some extent. If you're completely hands-off with your money, you may get bored very quickly.
If you're very distant from a company(e.g. a publicly traded stock) you are only required to put money in a portfolio and start clicking "buy" and "sell." All time apart from that is in the research and due diligence that will make buy/sell actions profitable. This is simple enough if you're working with a portfolio of large-cap, heavily traded companies.
But if you try to achieve a return similar to an early-stage startup on the markets, you generally have to look at tiny companies with low information and regulatory scrutiny; and the market for a penny stock is rarely fair and orderly, it's more likely to become an explosive, melodramatic war involving some combination of institutional manipulators(hedge funds and colluding market-makers), a corrupt company CEO, paid promoters and bashers on message boards, and stock flippers that rush in trying for the quick money. i.e. it's great if you enjoy theatrics with your gambling, or wish to learn the feeling of being a bag-holder.
(I excluded day-trading from this analysis; it's both so difficult to learn that most people dismiss it out of hand, and - once you do have a system, and emotions are out of the way - it's also kind of boring as a way to grow your investment. But if you approach it extremely patiently and systematically, it can work very well.)
So then, if you want a better chance of early-stage returns, you can probably do well as an angel. To do so means giving up a lot more time to meet the company leadership and work out a deal and monitor them, and it means having the funds available to have accredited investor status(which you presumably do). I'm not one to comment further on this, since I'm not in a position to be an angel. But I've tried everything else.
If you want the most direct control over your financial destiny, want to learn _all_ aspects of business, and want to continue doing some kind of work, you'd do best starting your own company. It doesn't have to be a web startup. It doesn't have to use a lot of initial capital either. You just need to be focused enough to create the all-important "something people will want" and not stray away into a hobby project or pure research. This can be as simple as buying up a form of property(physical, IP, etc.) that you think will gain value, and then working or paying some money to perform the actual developments/improvements; done well, this could be a lot less risky than betting on an idea and some founders.
The best part about the start-a-company option is that your risk is more incremental. You can try lots of things, as long as you don't spend too much on any one of them, and the whole time you are going to make money, learn something, or both, which is a great feeling. And you can pair up a business-building strategy with investments in public markets fairly easily, since money in the market is generally pretty liquid.