Choosing an exchange is definitely not an easy task. We should look upon various factors before choosing the right one.
I generally see how good reputed an exchange is followed by factors like liquidity, customer support, coins listed, the UI and UX etc...
If everything seems good only then I decide to deposit my coins in that exchange. The wise ones say that never put all your coins in a single exchange.
So we should choose multiple exchanges (2-4) and keep amount in all of them.