First, I would defer to @redbagofcourage who gave a great reply. I'm very much a newbie.
As I looked, I heard good things about Bittrex and Binance. I saw mixed reviews on Poloniex. I don't know anything about any others.
Most criticisms on any have been about getting registered and verified. There is also criticism about getting cash out. Of course, there are complaints about fees on all exchanges.