I've been using blockchain.info for years - i've never used a cold wallet once. Takes to damn long to download the blockchain!
No offence but that is pretty stupid. Why don't you just get some kind of hardware wallet like a trezor or a ledger wallet. That is a much safer option unless you are dealing with small amounts of Bitcoin. But blockchain is definitely the best online wallet.
Yes, blockchain.info is the best online wallet. Recently it is upgraded to the HD wallets. User experience is dramatically inhanced. There is
a review articles you could check out.