Is investing a good idea with a low amount of money?
Yes. I'll take the angle that you CAN invest in penny stocks. There's nothing wrong with that.
The (oversimplified) suggestion I would make is to answer the question about your risk aversion. This is the four quadrant (e.g., http://njaes.rutgers.edu:8080/money/riskquiz/) you are introduced to when you first sit down to open your brokerage (stocks) or employer retirement account (401K). Along with a release of liability in the language of "past performance is not an indicator..." (which you will not truly understand until you experience a market crash).
The reason I say this is because if you are 100% risk averse, then it is clear which vehicles you want to have in your tool belt; t-bills, CDs, money market, and plain vanilla savings. Absolutely nothing wrong with this. Don't let anyone make you feel otherwise with remarks like "your money is not working for you sitting there".
It's extremely important to be absolutely honest with yourself in doing this assessment, too. For example, I thought I was a risk taker except when the market tumbled, I reacted exactly how a knee-jerk investor would.
Absence of Perfect Assessment
Also, I feel it's not easy to know just how honest you are with yourself as we are humans, and not impartial machines. So the recommendation I would give is to make a strong correlation to casino gambling. In other words, conventional advice is to only take "play money" to the casino. This because you assume you WILL lose it. Then you can enjoy yourself at the casino knowing this is capital that you are okay throwing in the trash.
I would strongly caution you to only ever invest capital in the stock market that you characterize as play money. I'm convinced financial advisors, fund managers, friends will disagree. Still, I feel this is the only way you will be completely okay when the market fluctuates -- you won't lose sleep.
IF you choose this approach, then you can start investing any time. That five drachma you were going to throw away on lottery tickets? transfer it into your Roth IRA. That twenty yen that you were going to ante in your weekly poker night? transfer it into your index fund. You already got past the investors remorse of (losing) that money.
IF you truly accept that amount as play money, then you CAN put it into penny stocks. I'll get lots of criticism here. However, I maintain that once you are truly okay with throwing that cash away (like you would drop it into a slot machine), then it's the same whether you lose it one way or in another investment vehicle.