Good exchange is exchange that operated more than 2 or 3 years and they has good reputation, never get any hack and comply with the regulation in the country their located. I used Bittrex and Poloniex more than 2 years and i have balance in that exchange also since 2 years and untill now that my balance is safe. So this both exchanges is one of the best exchanges.
You're right what you said. But i don't recommend you to keep your money in exchanges which centralized and never give you the private key. Also they can freeze your money on any problem, even they won't tell you that. You just need to keep your money in the offline wallet.