The good thing with most Crypto exchanges (like Bittrex) is that the fee which they charge is in the form of a percentage (Bittrex charges 0.25% per trade). This means that you can begin to trade with as little coin as you want! however, you must take into consideration the minimum trade value of the exchange (Bittrex requires a minimum trade value of 50K Satoshi).
BTW: I use Bittrex as the example because it is the exchange that I use and the exchange that I recommend you to use.
Good luck and stay safe!
I do not limit my self to have a set minimum amount to trade to start on having trading. There is really no minimum or maximum amount in regards to starting a investment with the used of bitcoin because you could actually start as low as the minimum satoshi required on having a trade on some actual trading site. But if you have the resources , it is best to start big. Because the more amount you would invest the more profit and earning you could have in the future with just the proper handling and management.BTW: I use Bittrex as the example because it is the exchange that I use and the exchange that I recommend you to use.
Good luck and stay safe!