It is really risky having our crypto assets on an exchange, but this is the most convenient (and free means of storage of course), thus, exercising much caution is a necessity to take out certain security issues such as being phised.
Bookmarks are a great tool. Never under estimate the power of bookmarks. A lot of people has been saved many a times from phishing websites by these nifty bookmarks.
And don't forget to enable 2FA should the exchange be offering them. This is among the most effective means of making sure that no one else can log into your account except you.