What crypto exchanges can you recommend?
Binance and Bittrex are actually the two exchanges I can recommend personally right now. For most part of it, I will always recommend Binance any time any day, based on the fees, reputation, the chances of more development, the volume, the support, name them, all in one, that makes it a superb exchange to make use of.
However, you still need to understand that it is an exchange and you have none of your private keys which make you vulnerable to any thing that happens with the exchange in the long run, just as we saw with MtGox. Also, you need to always try as much as possible to keep your account very secured, as this is the best way you can at least not get screwed by hackers easily.