I`ve never used blockchain.info and i hate web wallets,but we have to use them unfortunately.
Every exchange trading platform is an online wallet and we have to rely on them.
I`m not very familiar with cold storage and offline wallets,but i should move to some offline wallet.
Diversification is the key, after so many scams and hacks over the years my rules are simple.
1. Never keep more bitcoins on any website than you are happy to shrug off if lost (BTC0.1 perhaps).
2. Keep a slightly larger amount in a secure local wallet (maybe BTC0.1 - BTC1)
3. The bulk in some form of cold storage, be it paper or hardware or both (BTC1+)