just like cryptsy that scamming people who store thousands bitcoin there ,
paper wallet is the most secure wallet to store your bitcoin ,
noone can get access to the wallet but you!
Not all of the exchanger are not legit and would just run away anytime, of course you are going to keep your bitcoins in a exchanger which is secure and trusted by the people, but it would be better if you are going to use it on Trading, because there is a possibility that your bitcoin will lost if you are just going to store it there.
Storing your bitcoin in a hardware wallet is the best one, because it is very invisible to the hackers since hardware wallet is offline, and you are just going to use it online if you are going to send bitcoins to other people.
Yes, you are right, keeping the coins in such a purse is the safest.
I used to store bitcoins in a web wallet, but I was told that hackers can hack it. I read about this a lot of articles