While there is no required amount to start in trading, there is a minimum amount that you can transact set by every exchange site. Like the example in Bittrex minimum is 0.00100000 BTC however if you trade with that amount I don't think you will feel the profit that you will earn from it so better increase your capital when you trade.
This is right mate. At least you have 0.001 BTC in exchange for fiat money excluding the transaction fees. But I guess this is just too little amount for trading. Anyway, to start with at least for an experience you can do it with this amount or little by little then increase gradually once you know the strategies in trading for more profits.