Storing your BTC on an exchange is the common way most traders save their coins. But is it the best method? Cold storage to me look expensive, since it is costive to purchase hardware.
If you dont want a cold storage because of its cost and also doesn't wanted it in some exchange, you can also use online wallet like blockchain and
coinbase, i also hear someone using freebitco.in to store there BTC because everyday he will received an interest by simply storing his bitcoin their which i think its a good idea, because if your not gonna use it, its better to stock it on a website where you can gain interest by simple storing it
I think coinbase is an exchange with bad reputation. Coinbase is not secure because it's an exchange. I read one thread in this forum that a lot of customers account got hacked.
For free and secure wallet use online wallets with keys.