I started with $1000. For me this was good because I could afford to lose that but it was enough that I started to follow what the market was doing and also paying attention to what causes the price to change. I studied market theory a few years back and it's amazing how different the real world is to what academics think should happen!
Anyway, the main problem is that the smaller your initial capital the greater return you have to make just to cover brokerage. For example, I use E-Trade which charges approx $33 per transaction. That means that just to break even your shares would have to rise to $1066 - if you're in it for the long term e.g. 5 years+ then that probably wouldn't be too bad but if you're hoping to get in and out quickly (i.e. trade) then you'd probably need more capital to avoid your profits being eaten up by brokerage fees.
As mentioned previously, the current correction has reduced the price of many company's shares from what they were a few months back so might be a good time to get in - although who knows how much further the market will fall???
Have fun!
Kloid