I want to learn a type of active investment trading. What types are there?

I’m interested in studying and becoming proficient in a certain type of trading. I just don’t know enough to know which type. I know there’s OTC, NYSE, NASDAQ, investing in individual stocks, commodities trading, derivatives, FOREX, what else? I’m not looking for a get rich quick scheme, just a way to earn a bit more money by studying and taking on a bit of risk. Does anyone have a handle on all the different types of trading, what an individual like me can do at home from my computer, investing small amounts—$1,000–3,000 to start? Are there any types of trading that’s involves less abstract thinking—more analysis of company or market conditions, versus higher math? Are there any types of trading that are more obscure, or less crowded with day traders?