Technically, it depends on your utility function. However, even without knowing your utility function, I can say that for such a low amount of money, your utility function is very close to linear, and option 5 is the best.

Here's one interesting way of viewing it that I once read:

Suppose that the option you chose, rather than being a single trial, were actually 1,000 trials. Then, risk averse or not, Option 5 is clearly the best approach. The only difficulty, then, is that we're considering a single trial in isolation. However, when you consider all such risks you might encounter in a long period of time (e.g. your life), then the situation becomes much closer to the 1,000 trial case, and so you should always take the highest expected value option (unless the amounts involved are absolutely huge, as others have pointed out).

As a poker player, the idea we always batted back and forth was that Expected Value doesn't change over shorter sample sizes, including a single trial. However you may have a risk of ruin or some external factor (like if you're poor and given the option of being handed $1,000,000 or flipping a coin to win $2,000,001).

Barring that, if you're only interested in maximizing your result, you should follow EV. Even in a single trial.

That depends on your utility function, specifically your risk tolerance. If you're risk-neutral, option 5 has the highest value, otherwise it depends.

Clearly option 5 has the higest mean outcome. If you value money linearly (that is, $12 is exactly 3 times as good as $4, and there's no special utility threshold along the way (or disutility at $0), it's the best option.

For larger values, your value for money may be nonlinear (meaning: the difference between $0 and $50k may be much much larger than the difference between $500k and $550k to your happiness), and then you'll need to convert the payouts to subjective value before doing the calculation. Likewise if you're in a special circumstance where there's a threshold value that has special value to you - if you need $3 for bus fare home, then option 1 or 2 become much more attractive.

That depends on the amount of background money and randomness you have.

Although I can't really see any case where I wouldn't pick option five. Even if that's all the money I will ever have, my lifespan, and by extension my happiness, will be approximately linear with time.

If you specify that I get that much money each day for the rest of my life, and that's all I get, then I'd go for something lower risk.

In general, picking the highest EV option makes sense, but in the context of what sounds like a stupid/lazy economics experiment, you have a moral duty to do the wrong thing. Perhaps you could have flipped a coin twice to choose among the first 4 options? That way you are providing crappy/useless data and they have to pay you for it!