You can use Binance, which is very easy to use:
[link to www.binance.com (secure)]

However, you don't actually need to use an exchange.

There are exchanges popping up left and right. Be careful.

You could purchase one of the major cryptos (Bitcoin, Ethereum, Litecoin, etc.) and then just use ShapeShift to get some altcoins. They usually have 40+ coins available. You could test out very small swaps using an app wallet such as Coinomi, if you don't have a hardware wallet. However, you should get a hardware wallet.