If you want to actually start a business designed to grow and make money, rather than simply a hobby that pays for itself, I recommend you start with a minimum of 20,000 to invest.
If you run it correctly (as a business), you can expect to grow your business, make back your investment, and begin making a profit in 3 to 5 years. Barring horrible luck, it will support itself without putting in more cash, and enable growth, within 1 year.