You can trade between different currencies on Poloniex, Bittrex and Kraken(to name a few) without any need of verification. This is what most of us new people do anyway. There are however limitations to the amount you're able to withdraw in 24 hours and sometimes there's a monthly withdrawal limit which can be frustrating if you strike it rich.

They are all a bit shady in their policies, especially Polo but we all use them cause nothing much better is available anyway. You go where the trading volume is at and for most currencies it's on the big exchanges.