Binance has demonstared trust over time even when they were hacked. Bittrex also seem decent and I am on a look for BitMax, they are currently doing well beyond my imagination.
I have no doubt using Binance. But Bittrex is now requiring KYC, so not using that exchange anymore. I used to trade some alts before in Bittrex. Other exchanges mentioned by the OP are popular ones. But even though they are known to the community, it is always better to safeguard your coins. So as much as possible, secure your coins in your own wallets.